According to Aristotle a tragic hero is a person of good birth who possesses the following traits:
- They suffer from hubris or pride.
- They make a mistake in judgment.
- Their circumstances change because of his mistake.
- They realize they are responsible for the new circumstances.
- They are punished more than they deserve.
If you apply these traits to Oedipus, you might decide he fulfills all of them. For example, he suffers from hubris because he can't believe he could be the source of the plague in Thebes. He also shows hubris when he kills Laertes, his father (though he does not know it) on the road because his father would not stand aside to let him pass.
When he decrees a harsh punishment for whoever caused the plague, he makes a mistake. His situation changes as it becomes clear he is the source of the plague because he killed King Laius. He also realizes he is married to his mother. When he recognizes what he has done, he takes responsibility for it and pokes his eyes out. He is also exiled from Thebes. You can decide if these were excessive punishment for his crimes.
Since Oedipus seems to fit Aristotle's criteria for a tragic hero, your thesis statement would indicate this. You will have to finesse the wording but you could say something like:
Oedipus exemplifies Aristotle's definition of a tragic hero because he is a person of noble birth who suffers from hubris, makes a mistake in judgement, finds his world suddenly turned upside down, takes responsibility for what he has done, and suffers excessively for it.
If you disagree with one or more of these points, you can remove them from your thesis statement. Certainly reword it to better fit your assignment or your understanding of the play. Then spend a paragraph on each of the points that show Oedipus to be a tragic hero.