I need to build a cheap temporary load bank to test an AC measurement circuit. I'm thinking of using a couple of 1250kW stove top elements for a load but I have a couple of questions. The elements are rated for 240 VAC. Can they be connected to 120 VAC (effectively half the wattage). Can they be connected 240 volt in parallel (half the current draw) and can they be connected 240 volt in series (double the current draw)

 

It will be a quarter of the wattage.
Remember power goes with the square of the voltage.

Also, your series/parallel understanding of the current draw is swapped.
For a given applied voltage Current increases with parallel, not series, loads.

 

1250kW stove top elements

That’s a big stove!