I don't know about the smell of puke, but there are those little carpet shampooer machines that work pretty good, What I did becuase my carpet was so bad was take it to the car wash, covered the underneath of my dashboard with plastic bags and hosed off the carpet with the high pressure sprayer. Then vacuumed the heck out of it, then left the windows cracked for a few days when it was parked.
It looks so much better.
