One of Oedipus' virtues is his strength of leadership. Simply put, he is a dedicated ruler of Thebes. When confronted with the plague that ends up creating misery to his people, Oedipus does not seek a politically expedient solution nor does he select a path of least resistance. Instead, Oedipus is committed to doing what can be done to ensure that his people are relieved of their pain. This virtue of leadership ends up challenging him to a great extent. It is this unrelenting passion for justice, for helping his people, for fulfilling his responsibilities of a good leader that helps to bring about his downfall and his descent from grace.
In Oedipus Rex, Oedipus' virtues lie in his cunning and unrelenting passion for the truth. When he was a youth, he solved the Riddle of the Sphinx and freed Thebes from one plague.
Oedipus prides himself as a savior. He feels superior to other men, prophets, even the gods. Pride (hubris) is Oedipus' greatest strength and weakness. Observe what he says:
When the riddling Sphinx was here
Why hadst thou no deliverance for this folk?
And yet the riddle was not to be solved
By guess-work but required the prophet's art;
Wherein thou wast found lacking; neither birds
Nor sign from heaven helped thee, but I came,
The simple Oedipus; I stopped her mouth
By mother wit, untaught of auguries.
Now Thebes is plagued by disease and suffering again, and (typical of a an arrogant man) he alone as King tries to reprieve his earlier glory. In this way, he speeds up his demise, for he is the cause of the city-state's suffering. He leads a manhunt looking for himself, the murderer of the previous King.
His dogged pursuit of the truth leads him to a mystery which he does not solve until his wife hangs herself. It seems that, by solving the first mystery (the Sphinx), it cursed him into not solving the second until it was too late.