How can I find the burnt dust-like odor in the house?
Obvious starting point: close all doors for a couple of days and see if you can isolate it to a particular room. If your place is an "open plan" design, this might still work, or you might need to hang plastic sheeting temporarily to isolate areas. After that, all I can suggest is trying one corner at a time to see if it's stronger in a particular area.

Actually, if you think it's electrical, youi mght want to try turning off circuit breakers for similar time periods and see if you can find it that way. Though if it is electrical and not obviously related to something like an electric stove, I agree that you probably don't want to spend too much time looking for it.