Bitty washes no problem. I spilt soda on one and it was no big deal.

If it got in the eyes this is an occasion where water is the lesser of 2 evils for the eyes. You need to flush them with clean water because soda is corrosive and sticky and will really mess the eye up. You do need to get all the water back out. I used a mini wet /dry vac to vacuum out 90% of it and let it air dry outdoors and face down(so the sockets can drain) for the rest.

If no soda looks to have gotten in the eyes, DON'T flush them because even water risks messing the eyes up.

While you are doing that to the head. The body can be taken care of like Nann said. Just tie up the neck, toss the body whole into a pillowcase , tie that up and wash it like any other clothes.