Buster,
I agree 100% with all the advice given above. Just a quick note because I tend to worry about all sorts of things…
I am assuming you are measuring these unbalanced voltages at the main panel and it’s likely a Poco issue. You mentioned lightning strike? That could certainly compromise a neutral at a buried splice or up at a weatherhead or poletop crimp.
If you are measuring voltages at other receptacles inside the house, and the panel voltages stay balanced, then maybe an open neutral in a MWBC??
Anyway, assuming it’s a Poco neutral issue… and your Line voltages to N are swinging to 85/135 at the main with one side loaded, it’s likely this residence does not have a great bond to ground like a metallic public water pipe would offer.
So, when you load one leg with a hair dryer (toasters work well too) be aware that you may possibly energize some of the local structure / appliances and it’s possible to get a shock or tingle when touching things like faucets. This is because your service bond is weak and you are creating voltage differentials / gradients with your swinging neutral. Think dryer frame to tub faucet. Just something to be aware of, especially with people other than you in the house.
Also, any other bonds to ground like a CATV shield may start to heat up as they struggle to keep your neutral at “zero”.
So setup your hair dryer test for troubleshooting and showing a Poco lineman. But don’t leave it running longer than you need to.
Full disclosure - I am an engineer and not a real sparky. But I did stay at a Holiday Inn once
If others think this advice is misguided I am happy to be corrected.
Good luck with the job.