Are the three unities observed in Oedipus?
As other commenters have explained, the three unities described by Aristotle are the Unity of Time (events should take place within a one-day period), the Unity of Place (events should occur in one locale, not many), and the Unity of Action (the drama should focus on one main plot only, without any focus on subplots pertaining to other characters).
Oedipus Rex adheres to Aristotle's Unity of Time because the events of the play occur within the space of one day. In other words, Oedipus is approached by the Priest of Zeus sometime in the morning, and by evening he has been exiled from Thebes. In fact, events really seem to occur as if in "real time" on stage, though some actions do take place off-stage (e.g. Jocasta's suicide) and are reported by a messenger.
The play adheres to the Unity of Place because everything happens on the palace steps. When Oedipus wishes to speak with someone who is not present, like Teiresias, the blind prophet, or the swineherds later in the play, those individuals are sent for and arrive at the palace to speak with the king. Likewise, before the play began, Oedipus sent Creon to the oracle so that his brother-in-law/uncle can return during this particular day (helping to achieve a Unity of Time) to this particular place (helping to achieve a Unity of Place). Oedipus doesn't go to where anyone else is; he sends for people he needs or he sends people to retrieve the information he wants.
The play adheres to the Unity of Action because everything that happens concerns Oedipus and his immediate investigation into Laius's murder and then his own history and parentage. Neither Jocasta nor Creon, for example, has a subplot or some minor story line of their own that exists simultaneously with Oedipus's.
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.