You have single phase 120/240 V service.

It is possible you have a dropped 120 V leg.

Any 120 V loads on that leg should not be working either.

You can turn the stoves breaker off and then back on to see if it has one pole not closed.

The next thing would be to check either the stoves receptacle, or open the panel and check directly on the stoves two pole breaker for both 120 V from each leg to neutral and 240 V between the legs.

DO NOT OPEN THE PANEL if you are not VERY sure of what you are doing.

You will be measuring voltages in a HOT panel and need to be careful to not touch ANYTHING else in the panel.

If he has measured before the meter, then he's had THAT open. The panel isn't worse.

My guess: one side of the service is open (corroded connection or somesuch) and one of the 240V loads in the house is providing a connection (albeit a resistive one) allowing the good leg to feed the open one.

My prediction is, if the original poster turns off all of the double-pole breakers, half of the 120V circuits will stop working.

In any case, the solution is to find where the connection is broken and fix it. If there is 240V at the line side of the meter, then the failure is at the terminals on the load side of the meter base, the terminals on the main breaker, the cable in between, or the main breaker itself. Failure inside the meter is theoretically possible but I've never seen it.

"If he has measured before the meter, then he's had THAT open."

Or he measured at a weather-head splice.

"The panel isn't worse."

Sort of.

There are a lot more things in the panel to touch accidentally than the few contacts in a meter base or weather-head connection.

Agree with shutting off all the 240 loads and seeing it one leg is back feeding the other.
The voltage might be a little low, but if the 240 V load is large enough it could still be within the normal 10% variation allowed.