There is a high pitch noise in background with MultiMix 4. It's a cheap USB mixer/interface. I have read others complaining about it, so there may be a quality issue with MultiMix. That thought was confirmed when I tried another USB interface, in this case Vox Tonelab ST (bypass mode without amp simulation). While it also has noise, it's more like regular noise type.
Luckily I was able to fix the problem by switching off input from ASIO4ALL settings for MultiMix. It appears that the input section is the culprit. Maybe it's just the fact that input is receiving a signal which can be affected by other sources.
I don't know if grounding would solve the problem. It's difficult to say since wall outlets in my room are not grounded at all. Yes, this is an old house. I've read people trying to solve similar problems with all sorts of ground wiring from the device to computer case etc. but I would be very careful when trying that kind of modifications and certainly wont encourage people to try it without proper knowledge. If you don't have grounded outlets there isn't a lot you can or should do.
I guess the issue can be just MultiMix 4. It's not the most expensive piece of hardware and maybe has poor protection against sources that can increase noise. However I'm not planning to buy another USB interface, because I can turn off the input and get noise free sound for mixing and also the noise doesn't seem to affect sound itself (only monitoring) so it's possible to record instruments.