How do I move a relative symbolic link?

You can turn relative paths into full paths using readlink -f foo. So you would do something like:

ln -s $(readlink -f $origlink) $newlink
rm $origlink

EDIT:

I noticed that you wish to keep the paths relative. In this case, after you move the link, you can use symlinks -c to convert the absolute paths back into relative paths.

This is a perl solution that preserves relative paths:

use strictures;
use File::Copy qw(mv);
use Getopt::Long qw(GetOptions);
use Path::Class qw(file);
use autodie qw(:all GetOptions mv);

my $target;
GetOptions('target-directory=s' => \$target);
die "$0 -t target_dir symlink1 symlink2 symlink3\n" unless $target && -d $target;

for (@ARGV) {
    unless (-l $_) {
        warn "$_ is not a symlink\n";
        next;
    }
    my $newlink = file(readlink $_)->relative($target)->stringify;
    unlink $_;
    symlink $newlink, $_;
    mv $_, $target;
}