This is a great question. As you know, the most important part of any essay is a strong thesis statement. In light of this, let me offer a few possible thesis statements.
First, you can write on the theme of blindness. This will be an insightful essay, because at first Oedipus is able to see and pretty sure of himself, but he is really blind. In fact, it takes a blind man to show him the way, Tiresias the blind seer. You can even make the point that the blind seer really sees. In the end of the play, Oedipus finally sees, but at this point he is physically blind. You can write a paper that argues that blindness is the path of sight.
Another possible thesis is to play with the idea of a tragic hero. Of course, Oedipus is a tragic hero. But what might be interesting is to ask whether any other character in the play has tragic qualities. Could Jocasta, the mother/wife of Oedipus be considered a tragic figure. If so, how? Aristotle's Poetics can help you here. You may want to start with his definition of what makes a tragic hero.
The tragedy of Oedipus Rex lies in the king's admirable search for truth and openness that meets with obstruction from those who would hide this truth--and from his own figurative blindness to the truth.
Since the thesis statement provides what is often called a blueprint (it provides the structure the writer will use to build the essay), it is important to include in this thesis the main points to be developed. With the thesis statement given above, then, the student can discuss the ways in which truth is obstructed by Tiresias and by Jocasta and not readily perceived by Oedipus.
The first to withhold the truth from Oedipus is Teiresias, who is reluctant to reveal the causes of the devastation and death in the city because he does not wish to bring misery upon Oedipus. Further in the play, Teiresias refuses to “reveal the troubling things inside me, which I can call your grief as well.” That is, the prophet Teiresias resists being the one to reveal the horrible truth to Oedipus for fear of incurring his wrath, although in his rage he later tells Oedipus, "I say that you are the murderer whom you seek"(l. 347). But just as he suspects, Teiresias is not believed and he does incur the wrath of the king. When Teiresias finally tells Oedipus the complete truth about the past, he prophesies what will occur to Oedipus (see ll.439-448).
Jocasta, too, withholds the truth from Oedipus. She is characterized as manipulating knowledge, at first shielding her husband from the truth that she foresees. She manipulates the authority of the oracles to suit the arguments of the moment. In one instance, she tells Oedipus that Laius's son could not have killed him because the boy's ankles were pierced and he was "left...to die on a lonely mountainside" (l. 678).
Finally, Oedipus, who has argued with Teiresias, begins to realize his own blindness to the truth. He recalls meeting a man where the roads toward Delphi and Daulia break from the Theban Way. Slowly, then, Oedipus puts together the memory that condemns him as he also recalls a drunken man telling him once that he was not his father's son. He also recalls a prophet predicting that he was a man who would marry his own mother "and shed his father's blood" (946). So, as he reconstructs the events of the past, Oedipus declares,
I think I myself may be accurst
By my own ignorant edict. (l.700-701)
Nevertheless, Oedipus insists on hearing the truth, again and again, in the face of reluctant tellers who are frightened for their lives, for his life, and for the future of Thebes.