I never tried the dishwasher. Since QOC sticks have strings on them, which get hopelessly tangled if thrown into a bag all together, we wash them in the storage containers we use.
About every 2-3 events [Yes, that often, otherwise, eww. ;-)], they are sprayed with a bit of soap or febreze and warm water. Then the lid is closed and the box is agitated, followed by rinsing, draining, and air drying.
If I remember correctly, even just washing them in a cloth bag with just the band ended up with a rat's nest to untangled since the straps would come undone while washing.