No quibbling helps here: the idea of eternal damnation, which had taken ever cleared shape in the Judaism of the century or two before Christ, has a firm place in the teaching of Jesus, as well as in the apostolic writings. Dogma takes its stand on solid ground when it speaks of the existence of Hell and of the eternity of its punishments.
When we look for definitive dogmatic teaching from the magisterium, there is surprisingly little (showing an awareness, perhaps, of the latitude of interpretation possible of the data of revelation). De fide, we know that it is the consequence of unrepented grievous sin; that it involves some form of punishment that lasts for all eternity. From the Athanasian Creed we learn that all those who have done evil will “go into eternal fire” and from Benedict XII (in the dogmatic constitution Benedictus Deus) we learn that the damned will be “tormented by the pains of hell”.
So, whatever it is, it is not pleasant. However, it is important to note that the language used in magisterial teaching using images of torment is rarely defined (in the dogmatic sense). For example, the idea of eternal fire is lifted straight from scripture; but we must be aware that the form that such eternal fire takes has to be metaphysically consistent with the state of existence of the damned in hell. Before the last judgement the occupants of hell are separated souls (i.e. pure forms); after the last judgement they have resurrection bodies (the form of which is itself a matter of much theological speculation). To see some of St. Thomas’s opinions on how this effects what “eternal fire” could be, take a look at what he writes in the summa contra gentiles about “How incorporeal substances may suffer from bodily fire” and at the section from the supplement to the summa theologiae on “The punishment of the damned”.
My own views follow the scholastic analysis that identifies the “pain of loss” (poena damni) and the “pain of sense” (poena sensus), with the first being the primary agony of hell. As the catechism puts it (para 1035) “The chief punishment of hell is the eternal separation from God”. As our supernatural end is the beatific vision of God, the eternal frustration of that end barring our way to actualizing us as we should be, what our hearts long for, is a truly awful prospect. About the poena sensus, I really have very little to say other than it exist and that to downplay it is probably mistaken; but much seems to be speculation to me.