I would have an electrician check thins out. Especially since you live in LA, and the air there can wreck havoc on outdoor panels. I use a APC 1250vA/740 watts one on my network gear. It lets me look at incoming and outgoing volts, plus how many "events". You should have an electrician put in a whole house surge on the main panel, or put this Leviton between the meter & meter pan. Make sure you get the correct one, or have the electrician you hire to do it. Some electric utilities will install them for home & business owners, then tack the charge on your bill to pay it off.
There is a 4-jaw & 5-jaw version. Your utility will know which one you will need.
Amazon.com: Leviton 50240-MSA 120/240 Volt 200 Amp, Secondary Surge Arrestor, Surge Protective Device 4 Jaw Socket Meter Socket: Home Improvement
As for checking voltage, most local libraries rent out Kill-a-watt units for their customers to use, to check what they are using on various appliances. You just plug it into the outlet, then plug the appliance in.
Checking the voltage with a meter is something that every home owner should know how to do. It is working inside the panels that you have to really know what you are doing. Otherwise if you ground yourself between one of the incoming legs or both and the Neutral or ground, you can kill or injure yourself.
I would shut off power to the house, go around and check every outlet and switch to see if they are "Backstabbed". That is when they just push the wire into the back, and the wire is held in place by a set of springs that push a jaw against them. They should be attached by the screws. GFCI outlets have a screw that pushes a clamp against the wire.
The biggest culprit is Aluminum wiring when you run into this kind of issue, along with backstabbed outlets. You can also check inside the panel for loose wires to the breakers, by flipping off the main breaker and use a flat head screw driver to tighten any that are loose, along with on the Neutral & ground bus bar.
I just use a $20 Sperry DMM for checking voltages when I find an issue. Otherwise it is just my 120/240/480 if I am looking to see if there is power or not at an outlet.
Having bad connections or brownouts, along with the utility controlling power to the home, can cause more issues then people realize.