I agree that no vomit smells anything but foul. It's a virus and it really doesn't matter what particular virus it is if they don't have any other alarming symptoms such as a very high fever. These things usually last about 24 hours. The thing to do is let it run its course.
We don't need food as much as people think, so stop the feedings/meals until things settle down. The main thing is fluids - both vomiting and diarrhea cause dehydration over time (like well after 24 hours), but putting anything in upset stomachs just causes more vomiting. Aside from the pain and the mess, all that stomach acid coming back up is irritating to the esophagus and throat, so you don't want to do that.
After several hours with no vomiting, try very small amounts of WATER. Just a few sips. Absolutely no milk or formula, absolutely no juice, absolutely no solid food.
If the water stays down for an hour, try a little more. You can try ice chips too if that works. After 3 hours, you can try a bit of a popsicle. I wouldn't do apple juice (diarrhea) or orange juice (acid). Some kids can use very very flat ginger ale - ginger can soothe the stomach, but you don't want the bubbles. But a 1 year old probably won't drink that, and maybe not a 3 year old. Some parents make a very weak ginger tea and let it cool off. Another thing some people try is Pedialyte. Do not give Gatorade - the high sodium and the food dyes are a problem.
However, if you are home with 2 sick toddlers, don't pack them in the car and go out to the store. Just use what you have. After 4-5 hours with no food and no recurrence of vomiting, you can try something very bland like crackers (saltines, nothing heavily flavored or with a lot of additives, no peanut butter crackers). If that stays down, you still have to wait, but then you go to the BRAT diet - bananas, rice, applesauce, toast (with a little jelly) or a small piece of turkey. No fruit, no dairy, no acidic juices, no high fiber (because of the diarrhea), nothing hard to digest. Keep the meals very very small, like tiny snacks.
Good luck!