[Galadriel55]

Ainur are not the same as elves, though, in this respect. It is true that the Fea of elves never dies, but they are "dead" to the outside world when they go to the Halls of Mandos. Maiar don't need to have a physical form, but they become people or animals (like Almesiva Moonshadow said), so that to become closer with Arda and Eruhini. They can exist in Arda without a body, though. An elve's fea would not be able to do that. When it is separated fro the body, it goes straight to Mandos.
During the Fall of Numenor, Sauron lost soe of his power - he could not change his physical form at will anymore. When Isildur chopped off the Ring, he lost almost all of his power and was not able to take a physical form again (it is possible that he would regain that power if he got the Ring back, but I'm not sure about this).