How do the elements of Greek culture contribute to the plot of The Oedipus Trilogy?
A good way of responding to this question would be to think of how the thematic concerns of this trilogy reflect some of the chief preoccupations of Greek culture. One of these that we can clearly see featured in this trilogy was the whole relationship between free will and the power of the gods in curtailing that free will. Prophecy in particular is a key way in which this theme is presented. Note the importance of such prophecies in Oedipus Rex: the play commences with Creon's announcement of the oracle at Delphi who reveals that the plague that is troubling Thebes will end when the city exiles the murderer of Laius. Prophecies follow thick and fast, with Tiresias, Jocasta and Oedipus all either giving or mentioning prophecies.
This leads to an exchange where Jocasta and her husband/son debate the validity of such prophecies. Consider the following quote from Jocasta where she urges him to ignore prophecy:
Fear? What should a man fear? It’s all chance, chance rules our lives. Not a man on earth can see a day ahead, groping through the dark. Better to live at random, best we can. And as for this marriage with your mother--have no fear. Many a man before you, in his dreams, has shared his mother’s bed. Take such things for shadows, nothing at all--Live, Oedipus, as if there’s no tomorrow!
The way in which they all do come true seems to support the principal aim of Sophocles to support the power of the prophets and gods, that had been under threat in his time. Sophocles therefore presents religious beliefs in his play, suggesting that in the face of the gods and their power, downfall and disaster could happen to anybody, and that we should try to live our lives in the light of this formidable truth as best we can.