What a great question! At the oracle at Delphi (the center of the Greek world) there were a few maxims that the Greeks thought were central to life. Two of them were: "know thyself" and "nothing in excess." If you think about it, Oedipus did not know himself and everything he did was in excess. The Greek would call this hubris. And because Oedipus was of noble birth and had these defects, he was a tragic figure.
In terms of wisdom, by the end of the play, he finally sees. This is, of course, ironic, because he is now physically blind. First, he knows himself. He knows who he is for the first time. He married his mother and killed his father. But on a more symbolic level, he is a mere man. Second, he comes to the realization that he is limited. He cannot solve all the problems, let alone his own problems. Hence, he learn moderation.
In a Greek framework, this would be called wisdom. Through suffering Oedipus learned to be a wise man.