You have, of course, identified what this play is absolutely famous for and one of the reasons why it is such a work of art. The play consists almost entirely of dramatic dialogue. But in this work what is left unsaid is often more powerful than what is explicitly expressed. Practically every line contains a possible double meaning or an ambiguity. This verbal irony serves to reinforce the dramatic irony of the play, as the main characters and even the Chorus only gradually come to grips with what is evident to the audience at the very start.
You might want to consider some of the following examples from the beginning of the play:
I learned of him from others; I never saw him.
Oedipus here talks of the old king Laius, who is actually his father and who he actually killed during an altercation at a crossroads, without ever learning of his identity.
Until now I was a stranger to this tale,
As I had been a stranger to the crime.
This speech of Oedipus is again harshly ironic, because it is both true and not true - he is a stranger to the tale as he does not know how deeply he has been involved. But at the same time, he is no stranger to the tale or the crime, as he is intimately involved and convicted in both.
It is this sense of irony that makes this play so gripping, as Oedipus plays the role of the detective only to find that the evidence increasingly proves that he is the victim he seeks. What heightens the irony in this sense is the number of hunting and tracking images that Oedipus uses to describe his pursuit of the villain - only to find that the person he is pursuing is himself.