For a long time I thought the grunting kind of noise from a bathroom back wall was a critter under the house. Not true. I don't hear it all the time, there is no consistency or particular time of day or night that I hear it. The panel is in a closet adjacent to bathroom, and the electric meter is on the outside in the area of this back wall and the closet where the panel is. This week, I caught it noisy enough, that I went outside, and heard the noise around that area. The box that holds the coax cables is in the same area, but it seemed to be coming from the meter. I could here it behind the brick.
I've heard this off and on noise in the four years I have been here. It's unpredictable, so it's hard to ask someone to come and check it out. It's like a grunt, - the best way I can describe it. I have not heard any buzz or humming that I know is associated with electrical lines.
Any clues? Any help is greatly appreciated. Oh... I sort of ruled out plumbing, because the plumbing for the tub/shower is in the opposite wall, and goes up.

I think you might get such a noise from an electric meter because there is an electric motor inside that spins. It's speed is dependent on how much electricity you are using at that time. If the motor bearings are worn or dry or otherwise worn out/defective, one could speculate that it could make a grunting/groaning noise.

If you're into experimentation, you could try turning on your clothes dryer, stove, oven, and air conditioner to really speed up the motor and see if the noise gets better or worse. Then turn everything off that you can and see if the noise changes. I think if you can confirm a correlation between energy usage and the noise that your electric utility should be able to replace the meter.

Best of luck,
WallyH

Not too get too far off the subject, but many years ago where I worked we had an outside storage area with wooden decks to put merchandise on... the area was covered with a shed roof. One winter day, an associate heard a meowing noise under one of the decks. We spent an hour cutting and tearing it apart carefully, not to injure this "kitten". Turns out it was the gas meter, and when the heat was on it "meowed"" as the inner mechanism turned. So yes, meters can make unusual noises.