Is the suffering of the damned eternal, or could the bodily punishment be finite (annihilationism)?

Eternally speaking, the damned will never see God; that is as clear as day in both Scripture and Church teaching, and it is eternal for the soul. What is left a little ambiguous is the physical punishment of the body in hell. Every evil person will rise on the last day in a body, according to John 5:28-29, and that body will be under some kind of punishment. But the Church also teaches that there are degrees of punishment in hell, based on how evil you were on earth, and there are only two ways to vary punishment: the intensity at a given time, or the length of time. The Church has not answered whether the greater or lesser degree is a matter of intensity or of duration. And once you allow degrees of punishment proportioned to a finite set of sins, the question arises how you can have an eternal punishment of pain for a finite set of sins; going pound for pound, once the punishment deserved is paid, that punishment is over. So the Church needs to answer these questions: either the pain is always there regardless, or at some point, once the deserved punishment is paid, the pain subsides and they go on existing without it. Some will say it is an infinite sin against God, but I do not think that is the way to look at it; you look at it juridically, according to what the sin actually deserves.