Diagnose cause of voltage fluctuation in house
120v is supplied as two "legs" of 240v.  In a perfect world, loads would be balanced and neutral would not be required.   Neutral is there to assure the midpoint stays the midpoint even if the two legs are not balanced (and they are almost always not balanced). 

A couple of volts of drift is no big deal, and is a normal and healthy effect of uneven loading on the legs (you could reduce it by using extra thick wire, but then you're wasting money).   

However, tens of volts of drift says the neutral is not doing its job, you have an open neutral or lost neutral.  This means balance is a matter of luck, and most of the time some appliances will see less than 120V while others see more than 120V, which is likely to damage the appliance and even start a fire.

240V loads such as oven, water heater, installed A/C unit, electric-car charger, heat pump, installed electric heat or electric dryer, will have no effect whatsoever on a neutral problem. 

The fact that neighbors are also having the problem helps.   What would help the most is if you have some sort of data-logging system actually recording leg voltages over an extended length of time.   Significant shifts in leg voltage (I don't mean 2 volts) would absolutely reveal a damaged or lost neutral.