Welcome to The Cat Site!!
Sorry we had to meet under these circumstances.
Have you looked all through the new place to see if maybe there is something he could have gotten into? New plants, something left in a closet, garage supplies, etc. If the place has recently been cleaned with disinfectants he could eaasily have been in contact with something toxic.
Is there new carpet anywhere? Sometimes the dyes in fabrics and carpets produce illness in cats.
Have you changed his foods? that might do it.
Is he a nervous cat?
It is of course impossible to tell from here, but with vomiting the main thing you need to do is make sure he isn't getting dehydrated, and stay aware of whether he is keeping any food down. It's now Saturday afternoon if you are in the US- not too late to get to a vet, and if he is vomiting that much it is certainly something to consider. If you don't go today and he gets sicker it might be Monday before he could be seen.
On the other hand, he could have just eaten a bug or something.
When you say 2-3 times a day since moving, how many days is that? If he is vomiting 2-3 times a day for one day it might not be a big deal, but 2-3 times a day for a week is getting to be a real problem. Cats have to eat, and they have to stay hydrated or else all sorts of nasty things happen.
So how long has it been, exactly?