Your typical microwave comes with a NEMA 5-15 plug, so it shouldn't plug into a NEMA 6-15/20 outlet... I'd start with a voltage reading from the outlet under load... Something smells of open neutral/multiwire circuit.
Nothing a pair of pliers can't fix...
Ian (Pulling a permit to rewire a Levittown House! <not> ) A.
Is there anyone on board who knows how to fly a plane?