In literature, conflict can be defined as a struggle between two opposing forces. This conflict can be external (between two characters) or internal (within one character). In this play, there are many possibilities as to what the main conflict.
You could say that it is Oedipus's internal struggle against the idea that he is responsible for the plague. You could say that the major struggle is between Oedipus and Tireisias and Creon since they say he is the cause and he doesn't think he is.
My opinion is that the conflict is more abstract -- that it is a conflict between people and their fate. I think that the play is about Oedipus's struggle against a fate that was preordained for him.
There are many conflicts in this story. This is what makes this story good. All good stories are complex. However, in Oedipus Rex, I would say that the main tension is between human freedom and the prophecies of the gods that Oedipus would marry his mother and kill his father. Oedipus thought he was clever enough to outwit the gods, just as he has outwitted the Sphinx, but in the end he is wrong. This is the most important conflict. Can a man defeat the gods? The answer is "no." I should also say that the Greeks were preoccupied with this tension on a broader level, and they believed that to exceed divine boundaries was to be "proud" and that the gods would act in punishment.
Where is there not conflict in this story? I think that Oedipus' predicament possess so much that is vivid in its depiction of conflict. On one level, I think that the conflict between what Oedipus has to do as a leader of his people and the inevitable collision this brings to his understanding of personal freedom. At such a moment, he has to subjugate his freedom to the will of his people. This brings about the horrific revelation, and the results which follow. Another such collision is between the idea of Oedipus' sense of pride in his ability to work through any set of conditions with his freedom when opposed with fated conditions. This would represent another conflict in the play.