On the enotes.com study guide for Oedipus Rex, I found the character detailed summary of Oedipus. I hope this helps you find the four character traits.
Oedipus, the title character, is the protagonist of the play. His name means "swell-foot" or "swollen-foot." One of the most famous dramatic characters in the history of western literature, he was singled out by Aristotle in his Poetics as the right kind of protagonist because he inspires the right combination of pity and fear. "This is the sort of man who is not preeminently virtuous and just, and yet it is through no badness or villainy of his own that he falls into the misfortune, but rather through some flaw in him; he being one of those who are in high station and good fortune, like Oedipus and Thyestes and the famous men of families such as these." Oedipus's fatal flaw, the technical Greek term for which is hamartia, can be thought of as a character fault or a mistake, or more like an Achilles heel rather than a flaw for which he can be held directly responsible. A hereditary curse has been placed on his family, and he unknowingly has fulfilled the terms of the prophecy that Laius's son would kill him and marry his wife.
The play's action is concerned with the gradual and delayed revelation of the fulfillment of this oracle. It specifically focuses on Oedipus's quest for knowledge, on the one hand, and, on the other, the other characters' resistance to discovering the truth; Jocasta tries to protect her husband/son from the facts, and the shepherd cannot be forced to speak until his life is at stake. Oedipus impatiently confronts Creon and Teiresias with their hesitation to answer his summons to the palace to share their knowledge with him and the public. Connected with this frustration is a feature of Oedipus's personality for which he is somewhat more responsible; Oedipus is also said to suffer from a character flaw known as hubris, or pride, and his cruel treatment of Creon and Teiresias in the aforementioned situations evidences this trait. He insists on hearing the truth, again and again, in the face of reluctant tellers who are scared for their lives, for his life, and for the future of Thebes.
Perhaps it is Oedipus's pride which rounds him out and allows Aristotle to hold him up as a well-fashioned character, since without it he would seem too virtuous and the tragedy would be too "unlikely." Oedipus's speech is also given a good dose of irony in the play. For example, when he calls for an investigation of Laius's murder and says "then once more I must bring what is dark to light," he is also foreshadowing his future blinding, since his investigation will reveal the dark secret of his parentage, metaphorically enlightened by the truth, but literally blinded by it as well. When he curses the murderer of Laius he is cursing himself and predicts his own exile and consequent life of "wretchedness." Oedipus is wise (he has solved the riddle of the Sphinx), revered by his subjects, and dedicated to the discovery of truth. He wants to rid Thebes of the plague (pollution, a common theme in Greek drama) that is decimating its population. Fate and the gods, however, have other things in store for Oedipus, and his helplessness and utter ruin at the play's conclusion are a painful spectacle.
1) Self-absorbed. He loves the praise he receives from the people of Thebes and even puts himself above the gods when he questions the people praying to the gods while pointing to himself as their savior.
2) Emotional. He puts his emotions before logic and gets angry with Tiresias and Creon when they confront him and tell him the truth. Instead of calming down like Creon and thinking things through, he gets heated and argues with them.
3) Prideful. His dialogue implies he feels he is invincible/infallible. When he hears the truth, he initially denies it quickly because he believes it's impossible that he would've been the murderer of Laius. He has that "No way! I am the King of Thebes, the savior!" attitude when he learns the truth.
4) Responsible. At the end when he accepts the truth he heard about himself, he curses himself and takes his eyes out, punishing himself. He decides to punish himself and cast the trouble on himself. He takes nobody down with him. He understands he is responsible for the curse over Thebes and for the death of Laius so he takes all punishment on himself.