What may be the purpose and significance of the interactions between Oedipus and characters like Tiresias and Creon?
It depends precisely what you mean. Speaking stylistically, the stychomythic single line exchanges encapsulate the sense of two opposing points of view crashing together: and one of the things the play might be considered to be about is the fusion of two incompatible things (think, for example of Oedipus as both father and brother).
In another sense, the exchanges are often fiercely interrogatory on Oedipus' part: Oedipus behaving like a detective grilling a prisoner, desperate to find the cause of the plague (again, you see, he is - at once - criminal and detective himself).
And, perhaps, most simply, the purpose of the exchanges is simply to reveal the plot: remember that the plot of Oedipus Rex drives forward, but at the same time, drives backward in time. What I mean is that, as the play moves forward, more about its historical back-story becomes clear.