I had ours dry cleaned at a "natural" dry cleaner. No odor and wonderfully fluffy.
I have a front loading washing machine and I don't know if I could even wash pillows in it. Long ago, I successfully washed foam pillows in a top-loader and was able to soak the pillows, agitate them a bit, then soak them again. I can't figure out a way to make sure they are fully soaked in a front-loader.