Oh boy those are some of the ugliest caterpillers! I had a bunch hatch out on my azaleas last year. They can strip a bush in no time at all. I prunned off the affected branches, smushed as many of the living ones as I could find. And then I sprayed everything down with B.T.(Bacillus Thuringiensis) at least once per week untill I was sure that no more were hatching. B.T. is good to use because it targets caterpillers and is not toxic to people or pets. Just keep it away from your butterfly garden if you have one. You should be able to find it in any garden supply store. I mix it in a pump up sprayer and saturate the affected plant untill it drips off the leaves. Dont forget to soak the bottoms of the leaves while your at it.
Good luck Cindy