Most texts, if they utilize irony, will use one or two types. Oedipus Rex, therefore, is unique because it implements all three types of irony in fundamental ways. The primary irony in the play is dramatic irony, which is when the reader is aware of something that characters in the story are not. The reader realizes Oedipus' true identity, his past crimes, and his incest much earlier than Oedipus himself and several other characters. Thus, when the reader sees moments such as Oedipus pronouncing death upon Laius' murderer and Jocasta stating that Oedipus favors Laius, he or she sees the tragedy of the story all the more clearly. In fact, this tragedy of ignorance is applied to every character in the play other than Teiresias, who is actually a prime example of verbal irony.
Verbal irony is usually characterized by if there is a difference between what is said and what is meant. In the story of Oedipus Rex, Teiresias is a "blind seer," which seems to be an paradox. Though Teiresias is physically blind, he has special insights into reality, which is how he knows that Oedipus is Laius' murderer. This irony between being blind and seeing is carried through the the end of the story when Oedipus brutally blinds himself only when he learns the truth and "sees" it for the first time. Thus, Sophocles plays with these motifs through verbal irony multiple times.
Situational irony, or when there is a difference between what is expected and what happens, also plays a heavy role in the text as a whole, especially as it relates to attempts to escape fate. When Jocasta and Laius slit the ankles of their three-day old son and leave him to die, they do not expect that their son could survive. Likewise, when Oedipus runs away from his adopted parents to avoid killing his father, he meets his birth parents and kills his father and marries his mother.
Sophocles wove all three types of irony into Oedipus Rex cohesively, and all three help to deepen this tragic tale.