Before I would worry about attempting to shield the noise, I would suggest trying to identify where it is coming from by shutting off various circuit breakers in the house. Once you identify a specific circuit, then start the process of eliminating appliances, lamps, wall-warts, etc until you find the problem. You may also be able to find the noise using a portable AM radio tuned to a station-free spot on the dial to search for the general location of the noise generator.
You mention it is intermittent. Is there any specific time of day when it comes on or goes off? Also, looking at your waveform image, it appears the pulse-rate is around 8.2ms. If my calculations are correct, that give you a frequency of about 120 hertz. It could be a full-wave rectifier diode somewhere that is producing the spikes when the ac signal switches. Of course this is assuming the values and settings shown on the scope are calibrated and accurate. Once you isolate the house power circuit producing the noise, you should begin looking for any wall-warts in it that may noisy.