What does it say about Oedipus and his feelings of guilt (or lack) that he clings to the illusion that Polybus was really his biological father?
This strikes me as a rather interesting question, but I'm not sure how much Oedipus clings to the illusion that Polybus was his father.
The suggestion from the drunken fellow at the party in Corinth that Polybus might not be Oedipus' real father causes Oedipus great apprehension and leads him to seek the Delphic oracle. The news from Delphi that Oedipus would kill his father causes Oedipus further grief and compels him to avoid Corinth and Polybus. When Oedipus learns that Polybus has died, Oedipus is relieved, because he thinks that he did not kill his father. The news, however, that Polybus was not his father again moves Oedipus into the realm of apprehension.
So, I'm not sure I see Oedipus clinging to the illusion that Polybus is his father so much as I see Oedipus hoping that Laius is not his father and wanting very much not to believe that Laius is his father.
As for what all this says about Oedipus, ti seems to me that Oedipus is responding in a common way when confronted with the possibility and/or accusation that he has done something wrong. How many people, when accused of some wrongdoing, readily and immediately admit their wrong? Oedipus is the leader of his people, but how many times have we seen our own political leaders or potential political leaders deny accusations of wrongdoing even when the proof of their wrongdoing appears manifest to everyone? Even though Oedipus is guilty of unnatural crimes, his initial denial of the accusations strikes me as quite normal.