After the lights came back on the lights are dim and the a/c won't run. I suspect one of the legs on the A/C service is opened up. An AC voltmeter reads 78-80, depending on which outlet I check in the house for voltage. I did a small experiment, shutting off every breaker in the house exccept for one single-phase circuit, and expected to see zero or 110VAC depending on which leg was out but I still got 78-80 on this one active circuit.

Any chance this is a problem on my side of the service or is this somethiing I should report to the power company? Should I leave my refrigerator running as it seems to be doing OK with no unusual sounds or smell?

Depending on the answer I'll know to call either the city or an electrician.

Was there ANY damage to your house? If not then there is about 100% chance it is not a problem on your side of the service.

The power lines from the pole to the house appear undamaged. Other than some good size branches falling on the roof there's no damage... none too big to do more than some shingle damage. It is possible a branch hit one of the wire from the pole I suppose.

It is possible a branch hit one of the wire from the pole I suppose.
Even then it is not your problem. I would call the power company ASAP and let them know of the low voltage condition.