i've washed them by hand with dawn and i've tossed them in the washer and air dried, both worked good. sometimes when you use the washer the spong will get turn around inside the mf but if you rewet it it'll go back to the normal shape.
i just toss them in the washer and dryer with my mf towels. if they're that dirty, just spray some APC and massage out as much of the dirt as you can under running water, and then toss them in the washer along with your mf towels...