Somehow, a directory named /transfer has had its permissions set to 0000. The directory is owned by root but, even as root, I'm unable to either change its permissions or to delete it. When I attempt to change permissions, using chmod 755 /transfer, the command completes without an error but the permissions aren't changed. How can I fix this?
My guess is that you have file system problem. As root, try executing the fsck command, and then try to chmod the directory or remove it.
That would mean although root owns it there are still no permissions to do anything. Boot to a live cd and delete the directory. Might work in single user mode but I doubt it.
I'd be kind of worried how that happened too.
Playing to the angels
Les Paul (1915-2009)