For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Oedipus and his daughter, Antigone, shuffle into Athens, where he realizes he’s finally come to the Promised Land, his final resting place. His suffering and exile should get the sweet release of peace soon. While he waits he meets the king and is also reunited with his other daughter, Ismene.
Act II
Creon, Oedipus’ brother-in-law (and uncle—long story) kidnaps Antigone and her sister Ismene in an attempt to lure Oedipus back to Thebes. He wants Oedipus to be buried in a sweet spot just outside of his hometown, where he can keep an eye on the tomb and stop vandals from defiling and angering the gods, but also outside of Thebes, where it might bring some more divine fury. Jeez, that's asking a lot. Can't poor Oedipus just die in peace?
Act III
Theseus, king of Athens, saves the girls. In return, Oedipus lets him know where his secret gravesite is so that Athens will always have a magical source of power. The earth swallows up Oedipus, painlessly. After crying it out, his daughters go to Thebes to try to sort things out there between their feuding brothers.