So what happens to murdered elves?
 

I know that elves are immortal. But what happened to the elves whose bodies were killed by, say, orcs? Like the faces of dead elves that Frodo and Sam saw in the Dead Marshes? Also, I believe there's a line in TTT that Shelob was guilty of drinking the blood of elves. I take it from this information that elves can die.

So, what happens to an immortal elf when his body perishes? Does his soul go to some sort of purgatory, doomed to wander aimlessly, mourning the loss of his physical body?

[?]

They physical self is damages, which prevents their souls residing withing; which pass to the Halls of Mandos?

[/?]

:)

It was my understanding that when an Elf who dies physically by means of grief or violence his soul passes to the Halls of Mandos, where he may remain as long as he likes before being either reborn as a child or simply being given a new body and returning to Arda.

The 'reincarnation in their children' was an early idea of Tolkien (found in, if memory serves, The Books of Lost Tales), but which was later dropped in favour of the latter 'scheme' mentionned by JennyH: after some time residing in Mandos and pondering about their past lives, they were reincarnated in their newly built bodies to live in Valinor. Only a few exceptions are known, e.g. Miriel and Fëanor. As far as I know, only one Elf ever returned to Middle-earth after dying and reincarnation in Valinor: Glorfindel.

Thank you for clearing that up, Earendilyon. I knew that only one of those was correct, but I wasn't sure which one.