What is the role of each character in these plays? What was the author's purpose for these characters?
Critic Northrop Frye says:
Tragic heroes are so much the highest point in their human landscape that they seem the inevitable conductors of the power about them, great trees more likely to be struck by lightening than a clump of grass. Conductors may of course be instruments as well as victims of the divine lightening.
So, by this definition, each of the tragic heroes in the trilogy are the "great trees" standing on the hill--human "conductors" of "divine lightning." The other characters, Jocasta, Heamon, etc... are the "clumps of grass" who are struck by the lightning after the the tragic hero. They suffer along with the tragic hero, often committing suicide.
In Oedipus, Oedipus is the great tree and Jocasta is the main clump of grass. In Antingone, Antigone and Creon (mainly Creon) are the great trees and Haemon and Eurodyce are the clumps of grass.