My GE Washer #WJRR4270EW44 is not agitating, but it is spinning, and so I assume that the motor is not the problem. However, in the week before it stopped, I did notice an oily smell when the washer was working. I was able to remove the agitator. When I removed it, it was not covered in oil (nor was there oil in the water), but the inside bottom of the agitator was a little blackish. Assuming that it might be mildew, I soaked it in hot water and bleach, which helped a little, but not much. I then washed it with dish soap, and that removed most of it, and so I am assuming that it might be grease/oil? There wasn't a lot, but I just want you to know what I saw.
I was afraid to go any further, and need help in diagnosing the problem, so that I can order the correct parts to repair it.