I have some 300W no-name PSU with 2 power sockets, one for PSU/computer itself and the second one I use for powering the monitor. In such a case, does monitor drain watts from the PSU?
I'm asking because currently I have AthlonXP 2000+ and voltages already barely fit within norms (12.8V@12V line, 4.7V@5V line, and 3.1V@3.3V line, on heavy load they get even worse, like 13.1V, 4.5V, and 3V). System is rock-stable yet, but soon I'm going to get AthlonXP 2500+ and overclock it to 3200+, so I'm worried that it won't work in such a circumstances... I had an idea of disconnecting the monitor from PSU and connecting it to the wall-socket instead, but I guess that it won't decrease the PSU load, right?

No, that power isn't drawn from the PSU's internal circuits. It's just passed through from the input socket, since the monitor needs 110 or 230V (depending on your country), which is exactly what's coming from the wall socket already.

Those voltages, however, are way out of spec. Did you measure them with a multimeter? Sometimes the internal sensors of the motherboard are not very exact, so the values in monitoring software are misleading. If your values can be verified with a multimeter, i would instantly replace that PSU with a brand-name one.

Thanks, that's what I thought.

No I didn't measure them with a multimeter, but the fact that voltages swing wildly as soon as there's heavy CPU and/or GPU work going on (I can even hear speed change of fans, though my mobo doesn't have any automatic fan-speed control), makes me think that the reported values are real.
A couple of years ago I bought 2 cases along with these PSUs, for about 20euro each, one of them already died in a puff of smoke, so it's a real crap. I guess I'll need to get a Chieftec HPC-360-302DF before new CPU