Why does Oedipus blind himself? Is this an act of weakness or of strength? Why does he ask Creon to drive him from Thebes? Does he feel that his fate has been just or unjust? Is his suffering, in fact, deserved? Is it partially deserved? Is it undeserved?

Oedipus blinds himself at the end of the play. Why he does so is not clearly stated, but there are a few literary clues that are helpful. When he has his sight, he is actually blind; he is blind in critical areas. Oedipus does not know whom he married, whom he killed, or who he is. We can say that he is blind when it comes to his identity. All of this is ironic because there is another character, Tiresias, who is blind, but he is able to see preternaturally. So, we see a juxtaposition of a blind man who sees and a person who can see but is actually blind.
When Oedipus finally realizes who is he and what he has done, he blinds himself. This act is also ironic because at the moment of self-realization and insight, he becomes physically blind (at his own hand). From this perspective, the theme of blindness pervades the play.
If we look at Oedipus’s blinding from a more emotional perspective, we can say that he blinds himself because he does not want to see what he has done, even if it was done unwittingly.
As to whether it was a sign of strength or not, I would argue that it is an act of courage. As we follow the story of Oedipus to the play Oedipus at Colonus, we see that Oedipus is a man of character and courage. Eventually, he becomes a boon and protector of Athens.

Oedipus blinds himself at the end of Oedipus Rex because he discovers that he fulfilled a tragic prophecy that said he would kill his father and marry his mother. Oedipus first heard the prophecy as a young man living in Corinth, where he had been raised as the son of the king and queen. He does not know that his biological parents, Laius and Jocasta, left him for dead after hearing the same prophecy when he was born. Oedipus thinks he is avoiding the prophecy by leaving Corinth, but he inadvertently fulfills it. He is run off the road by a large party, and he kills them all, including Laius, who he is unaware is his father. He solves the riddle of the Sphinx and is rewarded by being crowned King of Thebes. He is then married to Queen Jocasta (who is actually his mother). Over the course of the play, the truth is revealed to Oedipus, and he realizes what he has done.
The motif of blindness is important in Sophocles's play, so it is symbolically significant that Oedipus chooses to gouge his eyes out when he learns of his crimes. The blind prophet Teiresias is the first to tell Oedipus that the killer he seeks is actually Oedipus himself. He accuses Oedipus of being blind to the truth, while the physically blind prophet can "see" the truth of Oedipus's history. When Oedipus is aware of the truth, he physically blinds himself, essentially reversing his previous status.
Oedipus also explains that he wants to blind himself so he cannot look upon Laius and Jocasta in the underworld; he cannot face them after committing these sins against them. He does not want to look at the people of Thebes; he does not want to know how far he has fallen in their estimation or see their reaction to finding out that he was the source of the plague that caused them so much harm.
Oedipus feels justified in his self-inflicted punishment, and, again, it is symbolically just. However, the reader may also feel that Oedipus is too hard on himself because the prophecy determined his tragic fate even though he tried to avoid it. The fate that was given to him in the prophecy is unjust; there is no reason to curse Oedipus from birth with such a harsh life. However, tragedies also indicate a hero's tragic flaw, which is responsible for his downfall. If it had not been for Oedipus's quick temper, some of the events possibly could have been avoided.