From your picture, sewage from the rest of the house is filling the washer P trap. There's nothing wrong with your washer. I bet every time your washer discharges it stirs up the sewage sitting in the P trap emitting the stink. But even when the washer is not working there will be a slight discharge from the pile of sewage sitting in that open top P trap. It needs to be changed.

That black P trap needs to be removed. It probably was just a cleanout plug and needs to go back to a cleanout plug. From the looks of it, someone has already cut into the cast iron and put that white pipe in.

A good plumber will find a different spot to put the washer drain in without screwing up your vent system. Use a different plumber than put that washer P trap in!

There may be a basic problem in that your main sewer outlet goes through the wall rather than through the floor. It may work out a lot better if the washer was higher in the system. Is there a place on the floor above for the washer? A good plumber can then come down and maybe into that white pipe. Basically the washer needs to be higher relative to your sewage outlet.  Good luck.