If you go to your PM Inbox, and scroll ALL the way to the bottom, you will see the option to Download all Private Messages As xml, csv, or txt files. Do the same for your Sent Items folder, if you want to save those. I would recommend the text file version. Then you can simply do a bunch of Check All - Deletes until your inbox and sent items folder until they're empty.
As far as I know, there's no auto-delete for old messages.