Could be a bad connection of the neutral to the utility neutral.
The ground is connected to the neutral at your service and you could be getting a neutral-like connection to ground when measured with an Ohm-meter, but it won't carry enough current.
The electrician should check the voltage on the neutral line while there is an unbalanced load (all current on one side). If there is significant voltage on the neutral of an outlet when the power is on, then you have a bad neutral connection to the service.
If it is an open neutral, you should still get good power on 240 Volt loads like the water heater.