What you describe, that is some buzzing noise, doesn't seem like interference to me. You see, your wall plug is a fairly low impedance voltage source, so the equivalent source resistance is quite low. This means that it is difficult for one device plugged into the wall to interfere with another, at low frequencies like 60Hz or 120Hz (the buzz frequencies). Of course, you commonly do get interference from things like electric motors that power larger machines. I sometimes see this from my table saw for example, which has a 1.5 horsepower motor on it. But these machines take a lot of current, like 12 amps for example so they have the muscle to pull other loads on your wall plug around a little bit in voltage terms.
If you have something like a wall adapter (wall wart) or any kind of electronic device that plugs into the wall and it is buzzing, then you likely have an internal fault in that device that is causing a much larger than normal load on the internal power transformer. When a power transformer is overloaded it can buzz quite loud. This is due to a phenomenon called magnetostriction, which causes the iron plates to vibrate against each other at 60 Hz or 120 Hz (and harmonics of course). This could by what is causing your buzzing noise.