You raise an interesting question about whether it is possible for characters to escape their destiny. In the world of Greek myth, it is not possible. In fact, it is an attempt to avoid his destiny of killing his father and marrying his mother that causes Oedipus to leave Corinth.
Part of how fate works in tragedy is that the actions that lead to the tragic situation are inherent in the character of the protagonist. It is in Oedipus’ nature to try to master his fate. This is not bad – it is actually quite noble of him to give up a powerful position and rich heritage to try to protect his adoptive parents. That same character is what leads him to decide to pursue the cause of the plague in Thebes, no matter what the cost to himself. In a sense, it is Oedipus’ strength, determination, and desire to do the right thing that lead to his downfall (the downfall of an ignoble character isn’t tragic).
So, basically, the tragedy is caused by the fact that Oedipus isn’t the sort of person who would ignore the oracle and stay in Corinth.