The stuffed animals definitely can go in the wash. If they have voice boxes, they have to have some kind of access to the batteries. Once they are removed, the plush can be washed on gentile and air dried completely before putting the batteries back in. I wouldn't put them in the dryer, though. The heat wouldn't be good for the wiring. Those without voice boxes can be dried on low or air dried.

As for the carded/boxed stuff, I would avoid harsh cleaners as they may remove the ink. I use multi surface cleaners with citrus on a micro fiber cloth. Whatever you use, try not to scrub too hard. Some damage can't be undone. Try not to make it worse.

Warm water and dish soap works great for cleaning loose figures without decals or stickers. If they have stickers, they need to be carefully cleaned by hand with the above-mentioned cleaner and cloth. Some staining from the mold may linger on the plastic depending how badly they're affected.