Would people ever be casually compared to the gods in conversation?
That's two different questions.
Invoking the gods as an exclamation/interjection was common - di immortales, Iove, mehercle, ecastor & edepol are common examples found with the comedians (comedies give us the best literary approximation of everyday speech).
Not sure what you are aiming at when asking about comparisons - statements like "you're fairer than Venus"?