that certainly is a strange problem. The only thing i can think of is following the steps in that link you posted at the beginning. Along with that, it could still be caused by the updates? is this something you have checked? as if your server pushes out apple updates it could be trying to download a huge amount of data for the updates (this may not be the case but its worth a try) If you have had your server for less than a year you can phone apple themselves for some support which you get with it when you buy it. If not you could try phoning them anyway their normally quite helpfull and if its an issue they've seen before they will most probably be happy to help you.
Hope this is of some help, let me know how you get on :)
You may need to check your logs to see when they are being archived and at what time periods. You may also want to check to make sure that they are not left in debug mode.
You can use server admin to do this. Also if the Users' home dirs are on the same disk and you have network-based connections all of their cache files and browsing files will be stored on there if you don't re-direct them to a tmp folder on the local client when they log in.
The folder you mentioned earlier was the folder location for the software update server. This is where the software update service downloads its updates to.
Also remember that some files/folders are hidden and owned by root which means that you may need to resort to the terminal to delete/remove them. Using the sudo command will allow you to run commands as a super user (Root).
I'm not sure that the path can be changed for the swupd. I vaguely remember reading something about this but can't remember the outcome. Sorry.
Should be able to copy the entire swupd store folder to anywhere (ie: a volume with loads more space), then replace the original source folder with a symlink to the new folder...
Stop softwareupdate service, then do following in Terminal...
Then restart softwareupdate service.
sudo cp -Rp /usr/share/swupd /path/to/new/location
sudo rm -R /usr/share/swupd
sudo ln -s /path/to/new/location /usr/share/swupd