The three Unities in Greek drama, as described in Aristotle’s rules of poetry in The Poetics, are the Unities of Time, Place, and Action; here, the entire dramatic action of Oedipus takes place in a 24-hour period, since the exposition (the action before the start of the play), such as the confrontation of Oedipus and his father, the marriage to his mother Jocasta, etc., are all discussed as actions happening before the dramatic action begins, but are not acted out on stage. The entire play takes place at the entrance to Oedipus’ mansion – there are no interior scenes or locations in other cities, etc. (remember, this was before proscenium arches, set changes -- except for perioktoi --, etc.), and the entire dramatic action is Oedipus’ dilemma – there are no subplots or minor character developments/ distractions. Whether Aristotle was prescribing rules or simply describing already existing plays (by Aeschylus, Euripides, etc.) , the Unities became the criteria for "correct" dramatic construction for tragedies until the Renaissance.
As others have mentioned, the three unities in Oedipus Rex are 1) the unity of time, 2) the unity of space, and 3) the unity of action.
This is basically the recipe for the perfect tragedy described by Aristotle and which Oedipus Rex, a tragedy written by Sophocles in 420 B.C., follows.
1) The Unity of Time: Aristotle felt that a perfect tragedy takes place in the time period of one day. The events in Oedipus Rex take place within a day.
2) The Unity of Space: There should be one setting, or location, in the tragedy. Oedipus Rex takes place entirely in Thebes.
3) The Unity of Action: There should only be one plot. There is only one plot in Oedipus Rex; there are no side plots, no "side stories." The tragedy is that of Oedipus, the King of Thebes, who has fulfilled the dreadful prophecy of killing his father and marrying his mother.
Aristotle is a law giver and king Oedipus is his authentic hero.So the three unites are skilfully observed.