Oedipus Rex is engineered for disaster. Its tragedy could not have been avoided. Any choices made by Oedipus would only have slowed down the inevitable, not prevented it.
These kinds of questions are silly, really. Does anyone ever ask if comedy could have been avoided in a comedy? Could adventure have been avoided in an adventure?
Tragedy is guaranteed in Oedipus from the start: Oedipus is destined to suffer. Oedipus really has no choices once the play begins: he's a fictional character. His author, Sophocles, has all the choices, and he wisely chooses to drive the play according to the unity of time, place, and action. If he chooses to work outside any one of these three unities, the tragedy falls apart. It becomes something else: melodrama, not tragedy.
Oedipus has to demand the truth from Tiresias, the messenger, the shepherd, and Jocasta. If he stops asking any one of these four witnesses for the truth, the tragedy fall apart. He's already run away once (from Corinth to Thebes); he can't run away again.
Oedipus has no real choices that could have prevented his tragedy. All of the antecedent action has guaranteed tragedy: the oracles, the attempted murder of him by his parents when he was a baby, the murder of his father, his marriage to his mother, their four children together. All these events took place well before the play began.
The only REAL choice he has is to suicide (like Jocasta) or not. This is most profound philosophical and moral dilemma that anyone faces. In the end, I think, he chooses wisely: he only blinds himself. He chooses to live with his suffering, to be burdened by knowledge, to become a blind prophet like Tiresias. Oedipus chooses to become a hero.