Boy this is a tricky one.
I honestly can say I've no idea why the screensaver would be coming up, when it's ticked to never enable. As you said there's likely to be a 3rd party application causing the problem, though reading a description of what Onyx does hasn't elucidated the issue at all.
I'm not sure where to start, so we'll just go with the classic tests, if you'd be happy to bear with my clumsy troubleshooting.
1) Check the hard-drive isn't corrupted - you can verify this through SMART Utility:
http://cloudfront.volitans-software.com/smartutility314.zip
2) Verify Disk by opening Disk Utility, selecting the Macintosh HD volume and clicking 'verify disk' - there may be some volume corruptions causing OS X to not work properly?
3) If the above two steps do not demonstrate an issue, please could you click 'Repair Disk Permissions' on Macintosh HD through Disk Utility and then restart the Mac?
If that still doesn't fix the issue or indicate a problem, you can try an OS repair through the recovery partition. Hold Cmd + R on startup, and click 'Reinstall OS X' when you're in OS X Utilities. It won't affect any data or applications, and it'll only reinstall the OS X core files. This could potentially solve the problem if there's some weird screensaver kext that's corrupted or something ...
I really do appreciate your patience, please keep me updated and I'll sleuth the Internet for additional things we can try if this doesn't work!