Laius: He is the king of Thebes and father of Oedipus who was killed by his own son. He was informed that his own son will kill him and marry his wife, he asked his troops to take the son and kill him. Eventually they did not and left the boy to die with hunger and to b killed by animals.
Jucasta: She is the wife and mother of Oedipus, queen of Thebes. Before marrying to Oedipus she was married to Laius who was the king and father of Thebes. Jucasta appears in the final scenes of the play. She committed suicide in the end, may be with the guilt that she left Oedipus to die as a baby, thus leading to tragic end of the story. Jucasta is the mother of Oedipus children aswell.
Teiresias: He is a blind prophet led by a small boy he knows the truth about Oedipus origin. When Oedipus calls him to find out about the truth of Liasus murder he became ferocious to hear that Liaus was killed by him. Teiresias is often characterized as half man and half woman in classical literature.