What are the comparisons between Gatsby and Oedipus in their stories?
The original question had to be edited. I would suggest that resubmitting the second question might work out well. One of the strongest comparisons between Gatsby and Oedipus is that they believe in their ability to use free will to overcome any potential problem. Oedipus truly believes that he is able to solve the problems of his people. The plague and suffering that has fallen upon the people of Thebes is something that he believes he can "fix." He feels he can do this through his willingness to find the truth and restore order. Oedipus' own life has been filled with instances where his free will has "worked." Solving the riddle of the Sphinx, facing off threats to his leadership and his state of being, as well as being able to rule with power are all examples of this. Oedipus has faith in his free will and a sense of complete certainty that he can outwit anything that the forces of fate might offer.
Gatsby believes in his own notion of free will in much the same way. Nick describes Gatsby as one whose being "sprang from his Platonic conception of himself.” Gatsby is self made, reinventing himself from James Gatz to becoming Gatsby. In Gatsby's mind, his free will is able to shed the background of poverty, the horrors of war, and enable him to win Daisy. He has total and complete faith in his freedom. Like Oedipus, he fails to heed any larger configuration that might limit his notion of autonomy. He believes that he, and only he, can make any situation work to his advantage. Like Oedipus, he enjoys temporal success. Yet, also like Oedipus, it is not real because this success is "a promise that the rock of the world was founded securely on a fairy's wing.” This "fairy's wing" is what ends up defining the trajectory of both Oedipus and Gatsby.