Pain isn't actually mentioned by Bootstrap, as per the quote. But lack of human contact, long term, is psychologically bad for the human mind, and sensory deprivation is actually a way to break someone.
As to the sword screams--I would sometimes put that down to moonlight, or lack of. Notice that they seem fleshed and that flesh is an actual barrier until moonlight shines on them, and then it's not. This isn't consistant but I have noticed that to that whether they scream depends on their level of badassery. (Barbossa doesn't bother mostly, but other pirates do).
Nerve endings might not reach all the way to the surface of their skin in their current state. Neither does their digestive system work any more. The "corpsifaction" happens instantly (rather than rotting them away as though dead over time. Strangely, they do seem able to grip weapons and their fine dexterity, as evidenced by Jack running the coin between his..er..finger bones, means that on a practical level, they have to feel something, though it may be modified by magic.
So the pain may be momentary, a whisper of what it would have been to start with (and the whisper of being run through with a sword or hit upside the head would be dramatic indeed) and they cannot die from the wound, and likely revert to their original state within seconds. We know that this is true because Jack and Barbossa get run through in the first movie when they are in "zombie" state. Jack, after getting run though can likely at least feel when the repair is over--which is why, when he shoots Barbossa and the coin falls, Jack doesn't think he himself going to die, because he's just learned what the timing/window is before the reversion. It's not simply that the bullet is still in him--Barbossa BLEEDS, which means the flesh hasn't reverted. It is a little less than 30 seconds from when Jack shoots Barbossa, to when the curse is lifted. Here's the You Tube Vid for reference on the timing of that.
So my theory, based on what I have seen on screen is that they have to have some feeling, just to manipulate objects, and as reflex, but anything focused on pleasure fades, and pain is momentary--and in case of injury they revert to the exact state they were at the moment of the curse in less than a minute, barring limbs automatically reattaching.