3
It short - your hosting supports are stupid brain-damaged idiots!
I know. I have to say it in more "politcorrect" form, but... can't resist.
Silghtly more deep:
1)I see something strange in this path
/home/mack/public_html/kate/uploads/iroffer1.3.b10/upload
(from there "iroffer1.3.b10/upload" appeared in standard UPLOAD dir ???)
2) Shell commands executed under httpd account rights is bad sign, but - it can be result of
any compromised site on this physical host.
Can you show (here or me privately) result of
"ls - laR /home/mack/public_html/kate/uploads"
3) Consider any .avi as "malicious applications" is delirium, but you must check folder's permissions for UPLOAD (and even if you use WF|MyDownloads - disable write access for httpd in this tree branch... as temporary solution... and monitor folder status some time... Delete all content, ask hoster re-enable dir and contol it
4) Sentence "Xoops is one of those scripts that is hacked regularly" is simply big lie! You can (have) to ask hoster about documented and confirmed facts. If they can mix PHPNuke (one big security hole) and XOOPS - my apologies to boss of such support-man
"Probably #2 on our list of most highly exploitable scripts." Ha ... I can create any own private list... which will be useless scrap, if it will not have good basis
Finita la comedia
I think, host was hacked over any other site on this host (hole was found in phpBB some time ago, 2.13 was released for fixing it)... But can't be sure for 100%.
explore unusual (?) activity in UPLOAD dir, claim separate inverstigation on other hosts... (I don't know yet expoloits for XOOPS, which allow shell access to attacker), protect your sites with Protector (while I see in your case another type of attack)