Even though I have my own theories (which have some differences) about the Architect, the Oracle and how the matrix works.
Please, do share...!

Over the years on IMDb I built up a long list of my own explanations. It's probably too long for here but I don't know an easy way to cut it down. (I edited out the final
"FIGHTING TECHNIQUES AND STRATEGIES" section. That's the best I could do.)

Here are personal, sci-fi explanations for the matrix trilogy.
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THE HUMANS CANNOT DEFEAT THE MACHINES AND THE MACHINES WANT TO KEEP HUMANS ALIVE Q: WHY DIDN'T NEO USE EMP TO DEFEAT THE MACHINES?
A: Neo realized he could never destroy all the machines. In "The Animatrix" nuclear weapons were dropped right on the machine city and the machines survived. That tells us the machines can deal with nuclear blasts and EMPs because, nuclear weapons give off massive EMPs.
* Neo attacking the machines with EMPs would end any chance that Neo and the machines would work together to defeat Smith.
* Even if Neo could destroy the machines, where would the billion or so humans in the pods go? With a barren earth they would die from starvation.
Q: DIDN'T THE PROPHECY SAY NEO COULD WIN THE WAR?
A: Morpheus believed the Prophecy which said the One could end the war by going to the Source. But this story was created by the Architect which the Oracle tells to the rebels. After Neo met the Architect, Neo realized;
"The Prophecy was a lie." The purpose of the Prophecy is to get the One to the Architect.
Q: WHAT KIND OF POWER DO THE MACHINES USE?
A. The Architect tells Neo that the machines can survive without humans. What power sources could the machines use? Morpheus said that the energy from the humans was
"combined with a form of fusion". And we see that Zion is not powered by humans and the machines would know about that technology. So, the machines seem to recycle the heat and energy from humans and use this to power the matrix but the machine city can use other power sources.
Q: WHY DO THE MACHINES KEEP THE HUMANS ALIVE?
A. The machines can't just arbitrarily kill off humanity because humanity programmed them to serve. They're hardwired to serve humanity, not destroy it. The matrix is a means of preserving humanity on a planet not capable of sustaining life above ground. The machines are doing humanity a service by providing a "life" inside the matrix.
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THE ARCHITECT AND ORACLE AND HOW THE MACHINES DEAL WITH HUMANS Q: WHAT IS THE PURPOSE OF THE ORACLE AND THE ARCHITECT?
A. The Architect created the Matrix, but the Oracle got it to the point where it worked. They … keep the matrix functioning.
The Architect and Oracle, unlike Morpheus or the Agents, know what's really going on. They are computer programs who have almost equal, godlike, power. And they disagree about how to deal with the humans and the matrix.
* The Architect wants to keep the humans under control as much as possible.
Architect; "Your life is the sum of a remainder of an unbalanced equation… it is not unexpected and thus not beyond a measure of control." Oracle about the Architect;
"That's his purpose. To balance the equation." 'Balancing the equation' describes the Architect using computer programming to control human choice and keep the matrix running smoothly. The Architect's programming creates the Agents to keep the rebels from disrupting the matrix.
The Oracle believes in not controlling human choice;
Neo:"What's your purpose?"
Oracle:"To unbalance the equation."That the humans can choose to leave the matrix and that the machines and humans should cooperate.
Neo; "But why help us?"
Oracle; "I'm interested in one thing Neo, the future. And believe me I know the only way to get there is together."The Oracle's programming helps create the One to try to break the control of the Architect to allow freedom and peace.
Q: ARE THEY THE MOTHER AND THE FATHER OF THE MATRIX?
A. (The Oracle) studies how humans think and feel, the Architect's purpose is purely mathematical. In a real life family (not all the time), the mother is nurturing and the one who gets involved emotionally. Fathers are more reserved and think of things more analytically instead of understanding the emotion behind it… not always! But generally.
The Architect calls himself the 'father' and the Oracle the 'mother' of the matrix. Smith says to the Oracle;
"you would know mom". (Smith is trading insults with the Oracle after she calls him a
"bastard"). Smith seems to realize that as the Oracle has been helping Neo. She has also helped to make both the powerful Neo and Smith happen. So she is in a sense their creator or 'mother'.
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THE PURPOSE OF THE MATRIX, THE ONE AND ZIONQ: WHAT IS NEO AND THE "ONE"?
A. The Architect says to Neo;
"You are the eventuality of an anomaly. Which despite my sincerest efforts, I've been unable to eliminate…" "the anomaly is ... creating fluctuations in even the most simplistic equations."Anomalies or changes in the matrix program happen because the Oracle adds choice for humans. The minds of the humans in the pods are like computers hooked up to a network. As human choice changes the matrix program, the matrix is also altering human thinking and abilities. So, eventually as the humans are changing over time, someone wakes up from the matrix who is very different, the One, who can be in the matrix and be completely free of its control.
Q: WHY IS NEO ALLOWED TO LIVE WHEN HE WAKES UP IN THE POD?
A: The machines want the One to get to the Architect. So, they let people who wake-up from the matrix escape to Zion.
Q: WHY DO THE AGENTS TRY TO STOP NEO FROM GETTING TO THE ARCHITECT?
A: The Agents are not aware that Neo needs get to the Architect to reload the matrix.
Q: WHY DOES THE ARCHITECT WANT TO RELOAD THE MATRIX?
A: So the One sends code to the Source. This human and machine code inside Neo helps the Architect improve the programming of the matrix.
Architect; "The function of the One is now to return to the Source allowing a temporary dissemination of the code you carry reinserting the prime program…"Q: WHY DID THE ARCHITECT GIVE NEO A CHOICE TO RELOAD THE MATRIX?
A: The matrix works because of human choice. Neo has to make a choice for his code to have the correct thinking so it can improve the matrix program.
Q: WHY DOES THE ARCHITECT SAY THAT ZION NEEDS TO BE REBUILT IF THE MACHINES ARE ABOUT TO DESTROY IT?
A: If they did not destroy Zion and force them to rebuild, the population would increase to the point that it would pose a threat to the Machine World.…
* Why allow the humans to "rebuild" Zion? Because if Zion did not exist then the "One" will have no reason to choose the door that reloads.
Q: WHY DID THE PREVIOUS 'ONES' AGREE TO ZION BEING DESTROYED?
A: The Architect thinks the One would choose to rebuild Zion and stop trying to fight the machines. Because he says;
"Failure to comply with this process will result in a cataclysmic system crash killing everyone connected to the matrix" The fear of all the humans dying from the system crash persuaded the 5 previous Ones to chose to rebuild Zion. This strategy by the Architect worked, until Neo came along.
Q: HOW DOES THE MATRIX HELP THE MACHINES?
A. The humans in the pods must accept the matrix virtual reality program as "real" to have the correct mental state to produce energy and to have mental stimulation to stay sane.
Architect: "nearly 99% of all test subjects accepted the program, as long as they were given a choice."Q: WHEN 'IMPOSSIBLE' THINGS HAPPEN OR THE MATRIX IS RELOADED, WHY DON'T THE HUMANS REALIZE THE MATRIX IS FAKE?
A: While there may be memory wipes of any person who witnesses something "impossible", most people would try to mentally process the events in a way that would reinforce the Matrix's reality. The system uses the media to portray the rebels as "terrorists"… Also, as the Oracle explains in Reloaded, the system allows blue-pillers to perceive things beyond its control as supernatural…
When there is a "reload", the humans connected to the matrix could be put into a dream state. Also, human memories can be changed the same way Trinity learns to fly a helicopter in "The Matrix".
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THE POWER OF NEO AND SMITH AND THE MATRIX NETWORKS/WORLDS Q: WHAT IS THE SOURCE?
A: It is a machine network central ("mainframe") computer.
Oracle; "... The Source."
Neo; "The machine mainframe?"Q: RAMA IN THE TRAIN STATION TALKS ABOUT DIFFERENT WORLDS. WHAT ARE THEY?
A.
Sentinels
|
+-------+ +~~~~~~~~~~~~~~+ +-------+
|Matrix |~|Train Station |~hidden link~|Machine|
|program| +~~~~~~~~~~~~~~+ | City |
|network|-----main link----------------|SOURCE |
+-------+ +-------+
~ |
Zion ships Architect's room
This shows how programs can move from the machine city networks to the matrix computer program.
Q: HOW DOES NEO GET HIS SUPER POWERS?
A: Neo gets his power by connecting to the Source computer and partially controlling it. Then he is powerful with things that the Source can connect to directly, the matrix and sentinels. But he doesn't have super powers in the Train Station which has a connection hidden from the Source.
Q: WHY IS NEO MORE POWERFUL THAN MORPHEUS?
A: Morpheus and Neo have similar thinking but only Neo has the One code which allows Neo to have greater power in the matrix.
Q: HOW DID NEO STOP THE SENTINELS?
A: Since Neo is the One, he is connected to the Source… Being connected to the Source gave him the power to short their fuses.
Q: HOW DOES NEO MAINTAIN HIS LINK WITH THE SOURCE OUTSIDE OF THE MATRIX?
A: The Machine world must be covered with transmission receivers so that the machines can communicate with each other and the "Source" wirelessly. All Neo has to do is be in range of one of these receivers. The "One" code allows him access to this network.
Q: HOW CAN NEO MAKE A WIRELESS CONNECTION?
A: There may be technology in the large connector in his head which allows wireless communication using the One code.
Some believe that Neo stopping the sentinels means he's in another matrix program. But Neo can connect to the Source or machine central computer which allows him to control the sentinels;
Neo; "Tell me how I separated my mind from my body without jacking in? Tell me how I stopped four sentinels by thinking it."
Oracle; "The power of the One extends beyond this world. It reaches from here all the way back to where it came from."
Neo; "Where?"
Oracle: "The Source. That's what you felt when you touched those sentinels" Q: HOW DOES NEO END UP IN THE TRAIN STATION?
A: Since he was connected to the Source, he attempted to stop the Sentinels. He succeeded but was not ready for the power. He slipped into a coma, and therefore his command did not reach all the way to the Source and back.
Q: WHAT IS THE TRAIN STATION?
A. The Train Station is the connection between Matrix and one of the computers at the Machine world. This connection is 'illegally' established by the program called "Merovegian".
The Train Station also has to be more than a connection point. I am sure that Rama and Kamala don't have "Residual Self Images" (look like humans) while in the Machine World. … The Train Station must be a program that somehow takes their Machine code and turns it into Matrix code which gives them "Residual Self Images".
Q: WHY DOES THE NEW/STRONGER SMITH EXIST?
A: When Neo was 1st resurrected in the Matrix, Smith became something totally different. He was freed from being an agent... The Architect used him to balance the equation when Neo got stronger.
Some think Smith became powerful only because Neo changed him. Smith says;
"Perhaps some part of you imprinted onto me" But the Oracle also talks to Neo about Smith;
"He is you. Your opposite, your negative. The result of the equation trying to balance itself out." The Architect is trying to control the matrix. The Oracle explains the Architect's reaction to human choice;
"To him, they are variables in an equation. One at a time each variable must be solved, then countered." The Architect knows that through his design some computer program will become powerful enough to balance Neo's power. By chance Smith becomes that powerful program. This balances Neo's power and pressures Neo to reload the matrix.
Q: WHAT IS SMITH'S GOAL?
A: Smith wants to take over not only the matrix network (world) but also the machine city networks (world).
Oracle; "Very soon, he is going to have the power to destroy this world. But I believe he won't stop there. He can't. He won't stop until there's nothing left at all."Q: WHAT IS THE "SYSTEM CRASH" MENTIONED BY THE ARCHITECT?
A: The system crash happens if Smith destroys the machine computers.
Q: HOW DOES SMITH GET INTO SOMEONE'S BODY OUTSIDE THE MATRIX?
A: Smith infects Bane right before Bane exits the Matrix.
By Smith infecting Bane's virtual body he infects Bane's mind in the physical world. Then Smith connects to Bane's physical body with a wireless connection. This explains why Neo sees Smith's image inside Bane's body". This is possible due to Neo being connected (wireless) to the machine network and seeing all of Smith's connections, including Bane.
Q: IF BANE IS SMITH, WHEN NEO KILLS BANE, WHY DOES SMITH STILL EXIST?
A: Bane wasn't the original Smith,… It is the same as killing one of the Smith clones.
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THE END OF "REVOLUTIONS"Q: WHY CAN'T "MIS-BEHAVING" PROGRAMS LIKE SMITH BE EASILY DELETED?
A: Programs can hide in the matrix.
Oracle; "usually a program chooses exile when it faces deletion."
Neo; "Why would a program be deleted?"
Oracle; "Maybe it breaks down. Maybe a better program is created to replace it. It happens all the time. And when it does, a program can either choose to hide here or return to the Source."
Q: WHY DOES THE ORACLE LET SMITH TAKE HER OVER?
A: She figures if she allows Smith to be even more powerful than ever before, it will be too difficult for the machines alone to delete him… Smith doesn't only have the power of the Oracle, but of Sati and Seraph too. Therefore, this leaves the machines only one choice; to allow Neo to kill Smith in return for peace.
Q: WHY IS SMITH DESTROYED AFTER NEO IS TAKEN OVER BY SMITH?
A: * Smith and his clones can be seen as an exile program in the matrix that can hide from the Source. But Neo (while inside Smith) connects Smith to the Source (with a connection provided by 'Deus') and this allows the Source program to delete Smith and all of his clones from the matrix.
* In "Reloaded" Smith returned after being 'destroyed' in matrix 1. Why? To balance Neo's power. But in "Revolutions" Neo, while inside Smith, goes to the Source. So, because Neo is no longer in the matrix, there is no need for Smith to return to balance Neo.
Q: WHY DID THE MACHINES AND THE HUMANS NEED TO DEFEAT SMITH?
A: Neo tells Deus;
"The program Smith has grown beyond your control. Soon he will spread through this city, as he spread through the matrix. You cannot stop him." Smith would eventually have taken over the machine city networks and the Source. Smith's virus programming would crash the pod life support computers killing the humans connected to the matrix.
Q: IS NEO DEAD OR ALIVE?
A: Is he dead? When Neo is inside Smith, Smith is deleted from the matrix to the Source. This deletion clearly looks like it kills Neo's physical body. There is nothing in the movie that tells us that his body will be healed.
Q: WILL NEO BE SEEN AGAIN?
A: From the final scene;
Sati; "Will we ever see him again?"
Oracle; "I suspect so....Someday."They are talking about a time when they will see Neo again and not if his physical body is alive. The anomaly of the One will keep happening. The Oracle is guessing that a new One could have the personality of Neo. This is possible since Neo's mind was absorbed into the Source of the machine network. So, in the future his mind could be put into a new body.
Q: WERE ALL THE HUMANS IN THE MATRIX KILLED?
A: Smith did not kill all the humans connected to the matrix when he took over the matrix "world".
* The Architect and the Oracle talk about peace between humans and the machines. This is only possible if the humans survived.
* The Oracle also mentions the 'others';
"The ones that want out."Who wants out in these films? Humans in the matrix. So, again humans must have survived.
Q; WHY DON'T WE SEE HUMANS AT THE END?
A: Images from humans are being rebuilt because of the 'reload' of the matrix program caused by Neo's 'code' being absorbed by the Source.
Q: WHY DO WE SEE SATI AND SERAPH?
A: They are exile programs hiding in the matrix that cannot be erased by the Source. They are not changed by a reload of the program.
Q: ARE THE HUMANS STILL TRAPPED IN THE MATRIX?
A: The Architect (and the machines) agreed that the humans at the end of "Revolutions" have the choice to leave the matrix. The Architect says about the 'others' (humans who want to leave the matrix, see previous answer);
"Obviously they will be freed."Q: IF GIVEN A CHOICE, WOULDN'T EVERYONE REJECT THE MATRIX PROGRAM?
A: Would humans choose a comfortable life in a virtual reality (VR) world over a harsh life in a real world? A VR world could be as addicting as a drug.
Imo at least, BB ;-)