So far we've seen that he has the following powers:
--Create undead minions (his crew)
--Breathe underwater (assuming he needs to breathe at all)
--Limited teleportation (any area that is touching water?)
--His heart acts as a lich's phylactery
He has an artifact on board the Flying Duchman which allows him to call and control the kraken (I'm thinking that Lord Beckett wanted the heart so he could blackmail Jones into working for him, not to directly control the kraken with it).
And, of course, there's the Flying Dutchman itself, which can move underwater as well as on the surface of it.
I would definitely call Jones undead. His various aquatic critter-parts seem to be a result of sea life merging with his body, the same as with the rest of his crew.
As for his alignment, I would go with LE, since he is definitely fond of bargains, deals, and contracts--and twisting them to his favor ("you're free to go--as soon as we make port!").
His crew seem to share the same ability to teleport, although we've only seen them teleport from ship to ship...it could be some kind of Tree Stride-like ability, but it only works on wood. It might also be that they can only use this ability when Jones wants them to, otherwise he'd probably have a lot more runaways.