Many elements of the plot and the backstory are answered by the end of the play. We have learned the source of the plague, the identity of the murderer of Laius, and the identity of Oedipus. Jocasta has killed herself, effectively ending her part of the story.

One question that remains unresolved is the Corinthian dynasty. While it is obvious that Oedipus is is no shape to inherit his stepfather's throne, and also that as the son of Laius he has no claim to it, we don't actually hear of what will happen to Corinth. We do hear Creon agree to take care of Oedipus' children. We also do not know if the curse has actually been lifted or whether it will continue; we discover in another play by Sophocles, Antigone, that the Theban family is still cursed even after Oedipus' death. 

The other major question left unresolved is what will happen to Oedipus after he leaves Thebes. That question, though, is resolved in another play by Sophocles, Oedipus at Colonus, that tells of the death of Oeipus.