What characteristics does the characters of Oedipus Rex possess that does or does not allow them to deal with the obstacles they are faced with in their respective lives?
This is a good question. There can be several answers, but one characteristic that hinders the characters from progressing is the trait of pride or what the Greeks call hubris. We can see this very clearly in the character, Oedipus. Throughout the whole poem, Oedipus is convinced that he can solve any problem. Nothing is too big for him. In the past, he solved the riddle of the Sphinx and now he believes that through this efforts he can solve the problem of the plague in Thebes.
The problem is that Oedipus himself is the problem. He cannot see this on account of his pride. We can say that his pride blinds him. His view of himself is too high. He only sees himself as the solution, instead of the problem. In light of this, we can say that the characteristic of pride causes problems for Oedipus and the people of Thebes.