The unities of time, place, and action were derived from Aristotle's Poetics by an Italian theorist, Lodovico Castelvetro, in 1570.
In Poetics, Aristotle proposes the unities of time and action (unity of place isn't mentioned in Poetics) as guidelines rather than actual rules, which are based on what Aristotle observed in Greek tragic plays—not what he intended to impose on the writing of tragic plays. Castelvetro and French classical playwrights like Pierre Corneille, Jean Racine and Jean-Baptiste Poquelin (better known as Molière) interpreted these observations as requirements and adhered to these unities in their plays.
According to Castelvetro, the unity of time imposed a twenty-four hour time limit on the action of the play, the unity of place meant that the action of the play should occur in a single location, and the action of the play be restricted to a single, unified plot line:
Tragedy endeavors, as far as possible, to confine itself to a single revolution of the sun, or but slightly to exceed this limit. (Poetics, part 5)
In Oedipus Rex, the action of the play takes place in a single day. Even events which would take longer than a day, such as Creon's trip to the Oracle of Apollo at Delphi, are reported rather than actually enacted in the play.
Aristotle makes no mention whatsoever about a unity of place in Poetics. This unity was apparently devised by Cornielle as an outgrowth of the other two unities and Castelvetro's writings. The unity of place can also be logically assumed from the actual construction of an ancient Greek theatre, which limited the action of the play to what could reasonably occur in a single location. Nevertheless, Oedipus Rex conforms to this unity, in that the entire action of the play occurs in front of the palace at Thebes.
The only unity which Aristotle seems to have insisted on was the unity of plot, which he considered an integral part of a tragic play:
The Plot, then, is the first principle, and, as it were, the soul of a tragedy . . . [T]he 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, part 6–8)
Aristotle further imposed on the unity of plot that the action, the events of the play, must have a cause-and-effect relationship:
Tragedy is an imitation not only of a complete action, but of events inspiring fear or pity. Such an effect is best produced when the events come on us by surprise; and the effect is heightened when, at the same time, they follow as cause and effect. . . . Plots, therefore, constructed on these principles are necessarily the best. (Poetics, part 9)
Oedipus Rex is constructed around and driven forward by a single objective: find the person who killed Laius. Every event in the play is focused on this objective, and nothing that occurs in the play is extraneous to this objective. The sometimes surprising events of the play follow a strict cause-and-effect relationship that lead inexorably to the conclusion that the person who killed Laius is Oedipus himself.