Aristotle defines a tragedy as " an imitation of an action that...
Any discussion of the "three unities" in Oedipus Rex invariably includes reference to Aristotle's Poetics as the source of those unities.
In Poetics, Aristotle emphasizes only one unity—the "unity of action"—as absolutely essential to a tragedy.
Aristotle defines a tragedy as " an imitation of an action that is serious, complete, and of a certain magnitude" (Poetics, VI).
The important word regarding the "unity of action" is "complete," meaning that the plot should be self-contained, with a beginning, middle, and end, and that:
the plot, being an imitation of an action, must imitate one action and that a whole, the structural union of the parts being such that, if any one of them is displaced or removed, the whole will be disjointed and disturbed (Poetics, VIII).
It [a tragedy] should have for its subject a single action, whole and complete, with a beginning, a middle, and an end. It will thus resemble a living organism in all its unity (Poetics, XXIII)
In other words, a tragedy has a single, unified plot and no subplots.
Aristotle mentions the "unity of time" only in passing, as an observation, not as a rule.
Tragedy endeavors, as far as possible, to confine itself to a single revolution of the sun, or but slightly to exceed this limit. (Poetics, V)
Aristotle doesn't mention "unity of place" in Poetics at all.
The "three unities" as we understand them are derived from Aristotle's Poetics by French classicists in the seventeenth century. They believed that all serious French dramas should conform to the unities of time, place, and action—a single action occurring in a single place and within twenty-four hours, period.
In time, even these rules were loosened to allow scenes to occur in other locations that could be reached in twenty-four hours.
Nevertheless, Sophocles worked within these three unities in his tragic play Oedipus Rex, although he, like many other playwrights of his time, "pushes the edge of the envelope" regarding each of the unities.
Realistically, in terms of "unity of time," there aren't enough hours in a "single revolution of the sun" to accommodate everything that happens in Oedipus Rex.
Teiresias lives on Mount Telphosion in an area of ancient Greece called Boeotia, approximately twenty miles from Thebes. Oedipus has Creon send for Teiresais, twice and complains about what's taking him so long to get to Thebes:
OEDIPUS. Here too my zeal has nothing lagged, for twice
At Creon's instance have I sent to fetch him,
And long I marvel why he is not here.
Teiresias isn't there yet because he's an old blind man who needs a boy to lead him the twenty miles from his home to the palace, a journey that would easily take a full day for young, sighted man. For Teiresias and the boy—factoring in meal breaks, bathroom breaks, and occasional naps—the trip could take two days or more.
Later in the play, Oedipus sends for the herdsman who took the baby Oedipus to the mountains to die, but nobody knows for sure where he is:
JOCASTA. [A]s soon as he [the herdsman] returned and found
Thee reigning in the stead of Laius slain,
He clasped my hand and supplicated me
To send him to the alps and pastures, where
He might be farthest from the sight of Thebes.
And so I sent him.
The herdsman is in the "alps and pastures" somewhere, "farthest from the sight of Thebes," yet he appears just moments later to tell his story.
Regarding the "unity of place," the physical action of Oedipus Rex occurs in only one place: "in front of the palace at Thebes." Characters come and go from the palace, and the audience never sees them come from or go to anywhere else.
The imaginative action of Oedipus Rex—the action that takes place in the audience's mind—occurs in several locations far from and near to the palace at Thebes.
The audience imagines Creon going to and returning from the Oracle at Delphi, the baby Oedipus being taken into the mountains near Thebes to die, then being adopted by Polybus and Merope in Corinth, Oedipus meeting and killing Laius where three roads meet on his way to Thebes, Jocasta hanging herself in her rooms in the palace, and Oedipus finding her and poking out his eyes with the golden pins from her robe, and so on.
Unity of place isn't simply a theoretical limitation imposed on the ancient Greek tragedies. Even though Sophocles added the third actor to the performance of tragedies, there were still only three actors who had to portray all of the characters in the play, and the physical restrictions of the ancient Greek theaters simply didn't accommodate multiple changes in location. The actors, all three of them, couldn't go anywhere else.
The question of "unity of action" in Oedipus Rex raises one major issue.
The "action" of Oedipus Rex focuses primarily on "Who killed Laius?" However, at the same time that Oedipus and all the other characters are following the "Who killed Laius?" plotline, another issue arises—"Who is Oedipus?"
As the play progresses, the "Who killed Laius?" issue becomes secondary at times to the "Who is Oedipus?" inquiry. A considerable portion of the play is given over to this line of inquiry, even to the extent that the audience might forget that the main plot of the play—the "action" of the play, is supposed to be "Who killed Laius?"
Eventually the "Who is Oedipus?" issue is resolved, which, in turn, resolves the "Who killed Laius?" issue, but the question remains as to which of these represents the true "action" of the play and whether the action of the play is truly unified.