"Here I am myself-you all know me, the world knows my fame: I am Oedipus."
" Not I, I'm not the man to yearn for kingship"
"Our city reeks with the smoke of burning incense, rings with cries for the Healer and wailing for the dead."
Oedipus is showing hubris, and how he enjoys the power that being king brings him. He says the world knows who he is and how great he is and how he can solve everyone's problems. He likes being king, and wouldn't give it up because he likes the fame, and it's his only claim to it. Showing hubris also makes him a tragic hero, as it is one of the qualities, and could he even be counted as harmatia.
"How could kingship please me more than influence, power without a qualm?"
"I thought it wrong, my children, to hear the truth from others, messengers. Here I am myself-"
Creon is trying to show Oedipus that he doesn't want to be king, never has and never will. This makes him a foil to Oedipus, who highly enjoys being king. Creon does not show hubris, another foil to Oedipus, by saying that he is not ambitious and is content with what he has.
Pathos is being used in Oedipus's speech to be persuasive and to get his point across. He appeals to emotion by showing what a sorry state Thebes is in. This is opposite Creon, who prefers logic over emotion as a method of persuasion.
" Not if you see things calmly, rationally, as I do."
Creon uses rhetorical questions and logos to persuade Oedipus. He gives reasoning as to why he would never want to be king, with all that responsibility hanging over him, and rationalizes that it's not his cup of tea. Or whatever they drank. Probably alcohol.
Oedipus uses ethos to give himself credibility to his subjects as he tries to solve their issues. He says that he came to speak with them, instead of hearing it from others, showing that he really does care. A level of hubris is still present, where he sees himself above his subjects, or, "my children." This is what differentiates him from Creon in this regard.
Creon also uses ethos to show that he thinks of matters in a rational way, which would make him a clearer thinker, and therefore usually a better one. He does not have a side of hubris with his plate of ethos because he's not trying to put himself above others. He is simply stating how he thinks, and how that makes him credible, only trying to make himself look good.