All are in the LJ.XMLRPC namespace of course:
getfriendspage
sendmessage
setmessageread
getinbox
addcomments
These were gleaned from: code.livejournal.org/trac/livejournal/br
It seems only paid users can call addcomments.
This codebase is over a year old, it looks like they aren't using that repository. I believe there may be other methods. The iPhone app developer

The LJ support is useless. Is there another way to contact LJ devs? Anyone with XML-RPC client should implore LJ to update their documentation.