Is "Oedipus Rex" premised on the notion that Oedipus is bound or free? Is he the puppet of fate or the creator of his own fate?

The pull between fate (or destiny) and free will is a primary theme of the trilogy.  While modern thinking typically scorns the idea of a pre-determined fate, there seems to be something that attracts audiences to the idea that some things will go wrong, no matter what we do to try to redirect or change our lives. 

Freud wrote about this topic in The Interpretation of Dreams and the Oedipal dilemma. "There must be something, " Freud argues,

which makes a voice within us ready to recognize the compelling force of destiny in the Oedipus...His destiny moves us only because it might have been ours." 

Oedipus cannot escape some of his fate:  he does marry his mother and kill his father as predicted.  But what he does with his life after the prophecy is fulfilled is his decision.  He could have killed himself, but he chooses to go on.  He might have spurned his daughters, but chooses to embrace them. 

As Robert Fagles points out, "We expect to be made to feel that there is a meaningful relation between the hero's action and his suffering, and this is possible only if that action is free, so that he is responsible for the consequences." 

Sophocles' play, therefore, is a combination of both created and creator fate.