It sounds like you have a loose connection, very possibly a LOST NEUTRAL. A lost neutral is a serious problem. If the rest of the system, including grounding, is functioning properly, it may not be immediately obvious but will show under load. The key is to check your voltage.
Normal voltage is:
- 240V between hots
- 120V neutral to each hot
- 120V ground to each hot
- 0V neutral to ground
The overall numbers can legitimately vary a little. That's the whole 110V -> 115V -> 120V change. So if your numbers are 117V and 234V or whatever, that's fine. The main things are approximately 240V between hots (in some places, particularly multi-unit buildings it can be ~ 208V), the neutral to hot values nearly identical between the two hots - e.g., 117V and 119V is OK, 110V and 125V is not, and basically nothing neutral to ground.
- Turn off all breakers
- Turn on a 240V/120V combination circuit - e.g., typical clothes dryer - if you have one. If you don't, it gets more complicated because you want to be able to test 240V and both 120V legs - which could involved multiple circuits to get you everything.
- Test 240V (hot to hot) and each 120V neutral to hot. Make note of the values.
- Turn on some 120V loads, ideally all on one hot leg. Ideal would be a high current resistive load - hair dryer, toaster oven (regular oven is 240V so that won't help) or 120V space heater (which have a lot of issues, I don't recommend them in general, but if you have one then this testing is a great use for one).
If the neutral-to-hot values at a 240V/120V receptacle change significantly when you turn on or off an appliance then, based on the description, you have a utility problem.
Due to the way power is supplied and monitored, the utility may know automatically if all power (both hots) is out, may even know automatically if one of the hots is out, but very likely will not know if the neutral is out. But they will treat it as seriously as a regular outage, if they know it exists. Don't treat it like "poor power quality" (which can be a real issue). Treat it like an outage.