This is set up in Othello by long monologues by Othello's antagonist outlining his evil plan to ruin Othello. In Oedipus, the situational irony is set up because the audience already knows the entire story before they see it. The popular story allows the ignorance of each character's real situation become the irony of what they say. The main reason why the situational irony works so well is the fact that both characters are figuratively blind. Even their position in society, both of power, help the "attackers": Apollo against the city of Thebes in Oedipus the King, and Iago against the one who didn't promote him and possibly is sleeping with his wife in Othello. The end of each play is really what marks them as tragedies. In the end of both plays, the main character kills those who they love (directly and indirectly in both), either injure and outcast or kill themselves, and leave themselves with nothing, all because their tragic flaws came out in unfavorable circumstances, and they didn't make the right decision. .
The tragic flaws in each character come out many times in the course of the play. Sophocles sets up Oedipus' tragic flaw as pride. The prologue that the audience already knows sets up a reason for Oedipus to be proud- he has solves the riddle of the Sphinx. This great feat has landed him the job of king of the city of Thebes, where he married the recently-murdered king's wife and rules solely the city that now has a plague upon it. In his opening speech to the commoners of his city, Oedipus brags about his ability to be the only to solve the riddle of the Sphinx, and that he, of course for he is such a great ruler, will be able to get to the bottom of the reason of the plague and ridding the citizens of the misery they endure. The city fuels their king's pride by agreeing with him. The Oracle at Delphi proclaimed that the murderer of the king should be banished, and the plague will be lifted.