I am thinking about putting some kind of foam material to the wall in
the kitchen where the refrigerator is located. There's enough
clearance for a few inches of padding for sure.

Does anyone know where I can buy such things? I know I can get some
kind of adhesive sound reducing foam padding for computer cases, but
they are generally pretty expensive..

Yes. It's called insulation, and it's available at most home centers.
Or look in the yellow pages if you want someone to come in and blow the
stuff into your wall for you.
Even the normal stuff insulates from sound as well as heat - doesn't
have to be specific sound-reducing material unless you're a recording
studio, or unless you still can't insulate enough with regular
insulation.
Andy