Oedipus Rex has all the important elements of a complex tragedy and according to Aristotle, it was the most ideal play he had ever seen.
The protagonist, Oedipus, is the perfect tragic hero. He is a good man and more importantly, a good king. He fulfills the requirement of noble birth. His hubris aka tragic flaw is his pride.
To be considered a complex tragedy, it must have both a peripeteia (reversal) and an anagnorisis (recognition). Oedipus has both.
Finally, a great tragedy must result in a catharsis. This term been defined as purging or cleansing through the emotions of fear and pity. We fear what happens to the tragic hero because if it can happen to a person of such high standing then what about the rest of us? And pity because we do pity the fate of the tragic hero.
What makes this plot unique is that what happens to Oedipus is foretold. The Oracle at Delphi had spoken Oedipus's fate upon his birth and nothing anyone could do could change what was to be, not his parents sending him out to be exposed or Oedipus's own decision to leave his "parents" once he heard his fate.
Most tragic heroes, in a sense, have it coming because of their actions during the fall from grace, but not Oedipus. OK, so he killed the old man on the narrow mountain road when he was very young and had just heard his fate. His pride would not let him yield and the pride of the old man would not let him yield. He was his father's son, alright.
Once he answered the riddle and became king, he had proved to be a good and wise king who cared for his subjects. He cares so much that despite several warnings, he continues on in his quest for the truth until it becomes obvious. In the end, he, too, becomes a victim of fate.
You could take this in a variety of ways. I would think that one way would be to discuss the role of understanding and awareness that is present in the play. Oedipus represents the basic idea of "knowledge is suffering, while ignorance is bliss." Oedipus is a character who seeks to understand, seeks to gain knowledge at each step of his quest. Even when he is warned against such a pursuit, he has to know, has to gain the understanding of what is unknown in front of him. Due to this, his tragic condition is revealed as he becomes aware that he has killed his father and married his mother. This is something that is revealed to be uniquely tragic because of his own traits and condition. Another element would be to focus on how Oedipus is a wonderful ruler. It is Oedipus' willingness to end the plague that has descended upon Thebes that causes his tragedy to unfold. If he was not so devoted to his people, his tragic condition might have been different.
The point in the previous post that is so cogently mentioned about Oedipus Rex's especially noble nature constitutes the key to his unique tragedy. With this in mind, then, you can trace the development of the tragic events according to the paradigm of tragedy as defined in Aristotle's Poetics.
One salient example of Oedipus's tragic insistence upon the truth is his refusal to be swayed from it by anyone. For instance, when the soothsayer wishes to be dismissed, Oedipus will not allow him; when the shepherd tells the messenger in Scene 4 to hold his tongue, Oedipus scolds him instead,
No more of that! It is your tongue needs watching, not this man's. (1084)
And, when Jocasta, in her love, pleads with him to believe her in providing him a way from his imminent tragedy, Oedipus again refuses to take what he perceives as a coward's path. Even after he is found to be the cause of the plague, his being outcast is not suffiecient punishment: Oedipus as king inflicts what he feels is due punishment upon himself.