Measuring between ground and neutral with ohm-input sounds bad. Or at least I would not do that.

I have no idea what happens when you overload that just over 1 volt input, but that might be the reason for strange readings on the actual voltage channel.

Measuring current would be more interesting anyway. I have chinesium current transformers for that and i have made an extension cord with banana plugs in the middle (in a box, where i can have my mooshimeter safely) for easy installation to any device with a plug.

If removing that connection from ohm-input still shows that same waveform, i would measure between neutral and live next.

Is it possible to safely measure voltages (and current, preferably with a current clamp) at that ac-unit?