forgot one: which AIX-Version?

I would do the following:

make a fs backup or simply copy the /home directory away to an nfs-mount or tape or whatever

delete the filesystem

create a new lv (call it hd1 - makes it easier later on) with type: jfs2, create the /home filesystem just about 5gb smaller than the old one

add 1,6 gb to /user

add 128mb to /var

keep the left space free in the volume group, so you have some reserve the next time you get into trouble

restore the home dir

then clean up filesystems, clean not needed log-files, installation packages and so on

once you have the applications down, you could do the same with /home2, backup - delete - create jfs2 fs and restore

jfs2 provides the possibility to reduce size while applications are using the filesystem

if your os is aix4.3 forget the jfs2 thing, just delete /home and remake it 5gb smaller

don't forget to edit /etc/filesystems