3 domains – can i use different theme?

I have 3 domains (e.g. domain1.com, domain2.com, domain3.com) on one server. I want to show different content for users using each domain. I was thinking about testing the domain in the head section and based on it, i would supply a different theme. Is there any how to?
I could probably imagine how to do it, i just wander about one more problem – i also wonder about different permalink per each domain (different category prefix), but this would probably not work. Is there any workaround/plugion