Sauron's rehousing is different from an
Elf's rehousing: Sauron is a
maia, his body is like what clothes are to us: he can make his own body, in time, by meditating or the like: he just weaves flesh around his own spirit. Therefore, his body is made by himself alone.
Elves, on the other hand, are in essence spirit and flesh: they canot make their own body. Their spirit, if they die and wish to be re-born, is set into a new body (provided by an elf-man and an elf-woman in the good old way) by special grace of Illúvatar. It is not made by the Elf himself.
If you have to make your own body, like Sauron, and if you have lost power since you last made one, this diminishment will have an effect on the body you make: the first time Sauron was killed (in the downfall
Númenor) he lost the option of making himself fair; the second time, after
Isildur's finger-chopping, he lost the ability to have more than 4 fingers on his right hand.
Gandalf's re-housing after Zirak-zigil was speeded up and ehanced by a grace of the
Valar and of Illúvatar: that is why, allthough he had obviously lost some power in the fight against the
Balrog, the body he bore afterwards was not maimed in some way but actually enhanced.
Maedhros' re-housing would be entirely performed by Illúvatar, so his new body would not be affected in any way by whatever happened to him previously.
I hope this answers your question
