This is an interesting question because the only female character in the play who has a speaking role is Oedipus' mother/wife, Jocasta (Iocasta). Jocasta tries to mediate the dispute between Oedipus and Creon. Initially, she tries to comfort Oedipus when he worries about the prophecies that he will kill his father and marry his mother, but once she realizes that he is on the verge of discovering the truth, he tries to persuade him not to investigate the matter further.
Other women mentioned in the play include Merope, whom Oedipus believed was his mother. Because of the prophecy about sleeping with his mother, Oedipus left the house of Polybus and Merope in hopes of avoiding the prophecy.
Oedipus' daughters Antigone and Ismene appear at the end of the play, but do not speak. Oedipus is heartbroken when they are taken away from him at the end of the play.
Another female presence in the play that we should not overlook is the Sphinx, whose riddle Oedipus solves. In some ways, the Sphinx embodies the power that women have over men. Women drive and inspire men to take risks, to do daring deeds, and to inquire into difficult matters. Oedipus rose to his greatest heights when he solved the Sphinx's riddle.
So, in Oedipus the King, the roles of women are manifold: mediator, comforter, cautioner, objects of heartfelt affection, and inspiration.
In ancient Athenian society, the role of women was very limited. They existed primarily in the domestic sphere, and their lives were quite separate from those of men. They were normally married immediately upon reaching puberty, often as young as 12 or 13. That means that Jocasta in this play might have still been in her thirties when Oedipus married her.
Jocasta is seen in two roles in the play: she is a wife and a mother. Her function as a wife is obviously to bear children, but as the wife of a king, she also represents continuity of the hereditary monarchy and thus confers a certain authority or legitimacy upon her husband. It should be noted, though, that she does not herself chose her husband but is simply married to a man selected for her by powerful men. As a mother, her main responsibility is producing heirs. Her lines are mainly concerned with the maintenance of the family. She is concerned that Oedipus will cause suffering with his pursuit of a solution to the plague.
In the play, she is portrayed as passive. Although she ends up committing incest, she is discussed more as a carrier of ritual pollution than an active agent. Her suicide is a solution for her to the problem of her situation; we do not get a sense that there is any other possible form of expiation available to her.