I'd be inclined to consider three possibilities, possible coincident.
First, mindless undead like the zombie or skeleton. These are fairly clearly free of personality and move only clumsily. These undead are manipulated by magic, much like a golem (only it's evil magic). No soul, no personality.
Second, the aware undead. Creatures with minds and personalities such as ghouls and vampires. These creatures generally retain languages from life - but although they may have the same basic personality, they're largely evil. I think this is probably the Buffy/Angel model: the corpse has released its original soul, which performs certain functions like the consciense, and had it replaced by some evil spirit which has no conscience and is capable of warping the body, to some extent, to reflect its 'true' form. Look at the end of Season 2 of Angel (ironically, they only just screened it in my country) - you see what a vampire demon really looks like, and damn is it nasty. Also, consider Angel himself. He's 'The vampire with a soul', and he goes around trying to do good.
What does this model mean? The soul is fairly clearly released (nobody but Angel and Spike have souls). However, the soul does not dictate knowledge or personality; it seems to be the home of morality. Further, the demon that replaces the soul seems to be able to 'lay eggs' in its victims. A rather hideous thought.
Third, the voluntary undead. This is blurry. Things such as the lich cast aside their mortality for the price of a little skin and body odour. There's no way this is an 'infected' undead. The question is, Does it have a soul? If it does, you may well be looking at an archlich (the ultra-rare good or neutral variant). But why are they so rare? I suspect it's because voluntary undead cast out their soul and get a fresh spirit in its place. Again, the soul is unnecessary.
So, I think no undead have souls. However - this doesn't mean the soul is free; Devourers, for example, capture souls and feed off them. If so, where does the soul go? And is it dissimilar to the 'spirit', or sentience, of a being? (Theology now. Spirit is what sets humans apart from animals, which only have souls. The 'soul', it would seem, is not just morality but is lifeforce itself. The thing that makes your legs move or your hair grow.)
The spirit is quite definitely still held within the body (except for mindless undead); this would probably preclude raising until you blast the corpse to pieces. A lich would store its spirit in a phylactery. Most people would lose the spirit when they were killed, but it seems infectious undead can set up a 'spirit web' or something to ensnare their victims' spirit, like Trap The Soul or Magic Jar only with the body. Thus an undead cannot be raised until destroyed.
Whew, that's nasty. There is one possible 'out': assimilating the soul and spirit into one package in your theology, and claiming that the 'spirit' left in the body is just an impression, like a footprint in the clay. Thence, you can use True Resurrection on an undead person, and create a duplicate that's not undead, but only under this model.