Repairing (Aesthetically) a rusty washing machine and dryer
I agree with Ed Beal. If you want them back to Like New you'll need a can or 2 of Auto Stripper from an Auto Parts store. But, you'll treat the rust the same whether you strip them or not.

If the rust is light then a putty scraper to remove the paint blisters &amp; an S.O.S. pad or steel wool will take that away to get you back to bare metal. Or, best is to use a wire brush on a drill to get all of the rust spots back to shiny clean metal, this will open the paint blisters too.

Then, it's just a really stinky re-painting, no primer needed. So, good ventilation &amp; a large drop cloth with at least a 3-foot (6-foot preferred) clear perimeter are needed. The below Appliance Epoxy is unbeatable &amp; the spray version will get you factory results. Stay away from the lidded can version.

Finally, you'll need to address before or after the above, all of this excess moisture in the basement. If it's just the dryer venting into that area, then stop that nonsense immediately. Drill a hole through the top side of a wall &amp; run rigid vent piping, not any kind of hose or corrugated garbage. As short &amp; straight a pipe run as possible with an exterior sealing damper cap end.