STOP!
CPUID is wrong. BIOS is wrong. They're both WRONG. They're always WRONG.
Good lord, if your +12V was really 7V the damn PC wouldn't be running. This isn't a car alternator.
Both BIOS and software get their information from the same chip on the motherboard. This is one chip, in one location, located down stream via many traces, getting juice from one wire. This information is then fed through an algorithm to determine "voltage". Unfortunately, the algorithm is inherently, exponentially wrong.
The reason software and BIOS readings tend to be different is because they may use their own algorithims based on the chip used to monitor volts, tems, etc. (often called a Winbond chip because they're the ones that started implementing this feature) and come to their own conclusions.
The first thing to do is a simple common sense measure: double check the connection at the 24-pin. If all of those wires aren't making a firm contact, you can effect your OC and get bunk voltage readings.
If this doesn't improve OC, go ahead and try another PSU, although I doubt it will help. Could just be a problem with the RAM or motherboard.