Could Oedipus have prevented the prophecies from coming true?

Of course, since the story of Oedipus is a play, which is
a work of fiction, anything could possibly happen.  But it is important to note that
both Oedipus and Jocasta attempt to take matters into their own hands and defy the
prophecies.  Oedipus learns, while living with the man he believes is his father
(Polybus), that there is a prophesy that he will kill his father and marry his mother. 
He decides to leave and never return in order to avoid the prophecy's
fulfillment.

It is upon this decision that he actually
moves, unbeknownst to him, right into the eye of the storm.  He meets his true father,
Laius, on the road, and since both are too stubborn to give way to the other, they reach
a stalemate, which Oedipus solves by killing Laius.  He then solves the riddle of the
Sphinx which wins him the hand of Laius' widow in Thebes, Jocasta, who is his mother. 
So the prophecy is fulfilled as a result of Oedipus attempting to avoid
it.

Jocasta contributes to this when she gives Oedipus as a
baby to a shepherd to "dispose" of because of the prophecies that she learns
about.

For the Greek audience, the Chorus of this play is
teaching the important lesson that humans are foolhardy and disrespectful to imagine
that they might outsmart the will of the gods.  This implies that the prophecy is the
will of the gods, and, as such, is to be endured rather than
avoided.