I had this same issue! Especially with the boings, because they have wire in the center.
@Mizzely puts hers in the dishwasher. I don't have a dishwasher, so I use a grill brush when they're dry, then use a heavy plastic brush in the sink, I soak them with a little bleach in the water if they're really bad. I run them under very hot water to rinse, and spray them with f10 and let them dry. I have lots, so I can do a couple at a time and trade them out.
So far I haven't used enough bleach to alter the colors, so I'm not sure that step is even helpful, but I feel better about it.
I don’t soak the boings, they get the brushes, and water on the bad places, then f10. Be prepared to replace boings, because they will be prone to rust.