I like jjawn's suggestion. When I was in the same age range as your stepsons my mother had a mental breakdown. Showering/bathing would have meant that there had to be:
* a lightbulb that actually worked in our bathroom
* a gas account that wasn't delinquent for hot water
* towels that weren't molding on the floor
Yes, you can explain hygiene to a kid in the 6-12 age range, but if the mother is decompensating then the kids might be overwhelmed with just trying to get by as best as they can, period. Hygiene takes a backseat when you're that age and you're trying to get basic food, Mom's attention (good or bad), fumble through school, etc.
Offer to buy them the supplies they need, and send them home with backpacks with new towels, soap, shampoo. See what happens. That will tell you a lot about what's going on at their mom's house. But don't guilt the kids--don't make them MORE responsible for their hygiene than their mother should be. It hurts emotionally to have that burden placed on your shoulders at that age.