Where do they go? I mean, they're bound on earth with no further use?

We have no clue. It's likely that they're stuck into the soulgems until used, but after that... we're not sure if the soul is destroyed by enchanting or recharging, or if it's returned to Atherius/Oblivion and the energy used in enchanting/recharging is actually the result of the soul peircing whatever seperates Mundus from Atherius/Oblivion.

I've read a book once, I think, but I can't find it no matter how hard I look, so perhaps it just doesn't exist...

Anyway if I remember correctly and the book was actually in game then the bound soul would remain in the item it was bound too until the item broke (in case of DAedric weapons and armor) or until the charges would run out (in case of most everything else). You could imagine a constant effect enchantment would be one of the worst things. Daedra after being "released" return to Oblivion, so it would make sense for mortal souls to return to the dream sleave.

There's probably some sort of work-about with that, too.
In Feyfolken, the Daedra bound to the quill was strong enough to put it back together, after the protagonist snapped the object in two.

Dreamsleave? Aetherius? Oblivion?Soul Cairn?

Well we have some clues.

Umbra is still sentient within the weapon, but may be a special case on account of it is a chunk of Daedra. The Azura's Star quest in Skyrim implies that souls are still aware within their soulgems as well. I take these two points to mean that the dude you put in a black soul gem and enchanted a sword with is now your sword.

But enchantments fade and return sometimes, it seems. Just look at Volendrung.