Aristotle identified the characteristics of an effective tragedy, and Oedipus certainly fits the definition of a tragic hero. According to Aristotle, a tragic hero must have some sort of tragic flaw--which Aristotle lables as "hamartia." It is this flaw, he says, that is responsible for his downfall. The tragic hero is destined to fall as a result of this flaw, and therefore, his fate is unavoidable. (In Oedipus's case, his flaw is his hubris, or pride.)
In terms of the play and the time, Oedipus' fate was sealed. I agree with #2 that the message in this play is that your fate will be worse if you try to avert or avoid your pre-determined destiny--which is exactly what Oedipus did when he left the Oracle and headed away from his home in Corinth. In terms of life, we do have choices and we do have, it seems to me, at least some control of our own destinies.
Since the play is a Greek tragedy, and since the Greeks believed that our lives were controlled by fate, then I have to say there's no way Oedipus could have avoided what happened. In fact, you might begin to think that the moral of the story is that you'll get in worse trouble if you do try to outwit fate. What if Oedipus's parents had not abandoned him? What if the servant had left him to die? The play seems to be telling us to accept fate and go on.