Found the 2 below quotes by mistake when googling, relevant parts asterisked. How on earth does connecting a 240 V load make the missing neutral problem go away for the 120 V appliances?
I can answer this with experience. A long long time ago, (about 1987) we experience some weird happenings with our lights and whole house fan. The whole house fan is what tipped us off to the problem initially. It all of a sudden just slowed down. Some lights were bright, some were dim. The TV would not come on. After poking around a bit, i got out the (analog) meter and found some outlets had about 80 volts and others had about 144. ******Then, some how, i had the brilliant idea of turning on the oven. When i turned the oven on, the fan went back to normal, the lights normal. The 240v load apparently balanced the system.****** I was at somewhat of a loss at that point. I was not near as experience in electrical things at that time. I called an electrician friend of mine, he came down, poked around in the box some and decided to loosen the ground on the buss. "OH! GUESS WHAT? Fire on the ground" he said. I'm like "what's that mean"?. He said "well even though i've never seen this before, it sure looks like an open neutral. So i get on the horn with the power company. FYI, it was Kansas City Power and Light. They come out, and basically look at what i'm experiencing and the first thing the guy does is pull the meter. Then he measures the voltages on the incoming legs. All is equal. Then he tells me the problem must be on the inside. Puts the meter back in and the imbalance returns. "yep , he says, problem is on your side". So at this point, i'm at wits end, not knowing what to do, so I calls the fire dept and they say 'do you have a fire'? I says no, but I will, if someone does not fix this power imbalance. So that prompts a little higher level of action from KCPL, and they come out again. The service guy makes all his checks and then talks on the radio for a while. His supervisor says "you know that sounds like an open neutral". The guy comes back and says they suspect an open neutral. At that point, I explode. I said "NO SHIT SHERLOCK" I told you guys that 3 hours ago. They ran a bare wire from my meter can to the service box on the street and lo and behold, all becomes normal again. (did i mention i have underground service?) They came out the next day and started digging. About a foot from my water meter, at a depth of about 16" the neutral wire was corroded clean in half. Apparently it had been nicked by the backhoe putting in the water line 10 year prior. Well anyway, they fixed the wire, and all was good for exactly a year to the day. It was so weird, one year later, HALF the stuff in the house quit working. I had a dead leg. When they came out, i explained what had happened the year before and so they dug again. Sure enough, about 2 feet from the neutral problem, one of the hot legs had corroded in half.