How is Oedipus Rex an admirable character?
Oedipus is sympathetic and admirable for several reasons. He did not choose his cruel fate (to kill his father and marry his mother), but he still takes responsibility for his actions after he discovers how horrid they truly are. He laments his father's death and instead of killing himself when he discovers the truth about Jocasta, he blinds himself because he believes that death would be too easy a punishment.
While you could certainly argue that Oedipus's rashness and arrogance cause him to kill a stranger on the highway (who he later finds out is Laius), the Greeks would have believed that Oedipus would have killed his father at some point anyway because he was fated to do so.
In the end, the audience must sympathize with Oedipus over the loss of his parents and admire his willingness to exact punishment from himself. Afterall, he could have attempted to cover the truth about his identity as the king's murderer and his own mother's husband.
In my mind, the most admirable quality Oedpipus possesses is his commitment to the citizens of Thebes. He recognizes that his people are suffering and accepts his responsibility to do what he needs to ensure that their pain is alleviated. On many levels, this is powerful. The initial recognition of political self with personal self creates an image of the leader who is willing to ensure suffering for the sake of his people. Another level of positive attributes revealed here is that Oedipus possesses no fear in terms of acknowledging what has to be done. Consider the leader who realizes that his suffering will end that of his people. How many leaders would actually blind themselves, resign the throne, wander as a beggar, and endure humiliation in order for their citizens' lives to be better? Indeed, Oedipus has faults. Yet, one of them could not be his willingness to achieve a higher standard of leadership in the name of his people.