What does Oedipus Rex say about nature and fate?

Arguably, that what Sophocles is talking about that fate is not up to the person, it is the divine will of the God's.

The Ancient Greeks did not believe that fate was determined by the person, rather it was up to the God's. That is why no matter what steps Oedipus took, he was doomed to make the same mistake. Whether he knew it or not, even after persuing his investigation into the death of Laius, he had still married his mother, killed his father and bore children, so it could be argued that the discovery was always going to happen.

Fate is the divine will of the gods, and to believe otherwise in the Ancient world was considered hubris and an insult to the Gods. Which is why Euripedes was so controversial, but I shall leave that for another day.

It won't let me reference books so:

Antigone; Oedipus the King; Electra; (translated by H.D.F. Kitto; edited with an introduction and notes by Edith Hall. Oxford : Oxford University Press, 1994