I have a GE Model WHSE5240D1WW that keeps overflowing. When I run on a small load it fills all the way to the top as if it running a Super Load. It also run through the wash but does not run through the rinse or spin cycle.

SOURCE: GE Washer overflows

washing machines of any make or shape have a level sensor, this normally consists of a thin pipe from the lower end of the machine (where there is water) normally enters the bottom of the outer drum casing, this thin rubber or thin plastic pipe goes up to the top of the machine just inside the casing, it leads into a "pressure switch" a circular disc object about 50 cms in diameter on average, also this has about 4 to 6 wires on it, this thin pipe becomes blocked not allowing air to be forced up the tube into the switch, not switching the machine water flow off when it gets to the correct level empty the machine, drain off the water, unplug the power supply, and clear out this pipe, normally its congealed old soap powder, place pipe back as it was, checking for any leak holes in it, if damaged, replace it with new, run machine again to test long winded but i hope i have explained it thoroughly

SOURCE: GE WHRE5260E1WW Washer

The mixing valve needs to be replaced. It should be under $50 and is easy to do.

SOURCE: GE top load washer won't drain or spin

there was something stuck in the water pump. we pulled it out and good to go.

SOURCE: My GE washer wont stop

You have a problem with the water level switch.  It is located in the base of the machine below the tub.  Replace it and you'll be fine.

SOURCE: GE WHDRR418G1WW Washing Machine will not agitate or spin/rinse cycle

The ge wcxr1070t uses a coupling under the agitator . There is a cap on the top pop it off and remove the screw if you see one , otherwise just pull up , the coupling is under the agitator check to see if it is stripped . dr fixit in the repair service directory will have it if bad