Really sorry to read this, The Mailman

No one should be able to hack your vBulletin like this, regardless of the config.php permissions. Who is your hosting company? Do you run on shared, VPS, or dedicated?
Have you changed root/whm, cpanel, FTP, and all vBulletin admin passwords?
If you have a good hosting company, please ask them to run a malware scan on your server. If they won't, you can install & run maldet for unix. If you have an amazing hosting company, ask them to find logs showing who is doing what. Have you grabbed IP addresses yet? Perhaps they can narrow it down that way? If they won't, please write back here and I can give you some starting logs to glance at.
Finally, set up Host Access Control in WHM. Do not allow anyone to run FTP, cPanel, or WHM unless it's from your IP address. Again, let me know if you need assistance with this. I just went through the same thing. They're still trying, and failing now. So they can be defeated!
Good luck

This sucks.