Power Problum

Open neutral

Check the neutral wire connections over carefully. It may be open and the voltages you're measuring with the high-impedance multimeter are a result of it floating to more or less arbitrary voltages. If the neutral is open, the individual leg voltages may be wrong but the voltage hot to hot should be steady and correct at a nominal 240 volts...or, in rare instances, 208 volts if it's two legs of a three phase Y supply.

Obviously, don't use the extension cord until you get it sorted out properly. An open or high-resistance neutral can cause all sorts of damage to things plugged into the circuit as the voltage fluctuates rather wildly.

You have a bad neutral. It could be a bad connection at either end of your cable, or a break in the cable. Check the voltage between the two hot legs, it should be very close to 240 volts. You cannot rely on adding your readings from each leg together. When the neutral is compromised, voltage on each leg will fluctuate wildly whenever any load is introduced, including your voltage tester.

Check your connections. I would be willing to bet you have a cat whisker jumping between two terminals.