A custom ROM effectively replaces everything on your phone except the bootloader. ROMs aren't compatible with a particular version of Android, they ARE a particular version of Android. All you need to know is whether the ROM you want to install is compatible with your phone.
Once you have installed a 3rd party ROM, it is usually not a good idea to apply any more updates from anyone except that ROM developer. So what you said was absolutely correct. Stick with either only stock ROMs or only 3rd party ROMs but don't try to mix the two.
So, once you have installed the Omega ROM, the only updates you should apply would be to keep re-flashing whatever is the latest version of the Omega ROM.