When our fridge is plugged in, the voltage becomes unbalanced. Beforehand, L1 and L2 are both 120 VAC to neutral. After plugging in the fridge, L1 goes to 70 VAC and L2 goes to 170 VAC at the breaker box. The fridge appears to be OK because it will operate fine from our garage (on a separate service).

a522,
The last time I saw what you're describing the neutral or grounded conductor at the connection outside the dwelling where the utility laterals connect to the service cable had come apart...
Take a good look outside at your point of connection... should be three wires, two of them are insulated and one is bare, even if this connection appears to be good you should consider calling the utility to come and check these connections.

If it's not outside it could be inside in your panel... but be careful if you move a conductor under load you may get a large ARC... If you can shut off all the breakers in your panel and still see to safely, check the integrity of the neutral conductor connection... it least you could rule out the panel.

As always if you're not comfortable working in a live panel call an electrician!
Be Safe

Bad service neutral. Call the power company immediately!
Then if they don't find anything call an electrician.
This is not a DIY fix.

Thanks for the advice. The neutral connections were tight, but the direct buried neutral wire from the pole (meter) to the house (breaker box) must be bad underground. We ran a new neutral wire this morning, and it fixed the problem.

How did you run just a new neutral??
If you did that was not complaint.

We just ran it temporarily for troubleshooting purposes. It has since been removed. Now we are making plans to dig a 200' long ditch and run a completely new power feed. We just wanted to make sure that the neutral wire was really the problem first. Our utilities have been called to identify exactly where the phone line, water line, and existing power feed cables are located, before we start digging.