Two predominant conflicts in Oedipus Rex are Human against Fate and Human against Self. All through the play, Oedipus, in a Human against Fate conflict, is unwittingly chasing the very fate he is trying to escape. Indeed, Oedipus was meant to be left as dead as an infant for the purpose of outwitting and escaping fate. As Oedipus's actions in the end of the play and his final exile show, he wholly and completely failed to escape his fate in any way. Therefore, Sophocles makes a strong statement advocating the power of Fate over humankind.
O cloud of night,
Never to be turned away: night coming on,
I can not tell how: night like a shroud!
Oedipus struggles in an inward direction throughout the play against his hubris, which is defined as excessive, detrimental arrogance and pride. This hubris is his tragic flaw and the substance of his Human against Self conflict. It is Oedipus's hubris that leads him to require the disclosure of the fateful information held by Creon and Teiresias. It is, likewise, his hubris that leads him to swear to discover the identity of the murderer of King Laius and punish him fully. The conflict of Oedipus against self here, of course, is that Oedipus himself is the murder and the one whom he is sworn to discover and punish.
Again, it is clear in the ending of the play that Oedipus is wholly and completely incapable of coming out of this conflict victoriously, even though he has opportunity to step away from the conflict--he fails to do this because he fails to recognize there is a conflict, because he fails to recognize his hubris. Therefore, Sophocles makes a strong statement about our helplessness against our own inner flaws, about which we are blind--unless someone, like a Creon, can convince us to see rightly.
Then once more I must bring what is dark to light.
You shall see how I stand by you, as I should,
To avenge the city and the city's god.