First disclaimer: This replay contains some possible (if insane) suggestions and is not short.  Those with short attention spans might want to skip this one.

Big disclaimer on this one, Fred.  Just about everything I can think of that might be strong enough to get the smell of vomit out of wood could possibly harm the instrument.  Probably the best possible course of action is to take it to a luthier and ask if they can fix it.  I wouldn't take your first-born along when you go to get that estimate.  I don't know what that sort of a repair actually costs, or if they even have methods for it, but I wouldn't think anyone would want to work on that sort of a smell for low pay.  LOL

Never dealt with this particular sort of problem, I am not a luthier, and so all suggestions I make here should be considered just plumb coon crazy and for entertainment value only.  Anyone trying them is at their own risk and shouldn't take a baseball bat after me for mentioning them or Pierre for owning this forum, etc.  K?

Worst case scenario, if nothing else works.. You could take off the top so you could wipe the inside down with something like lemon juice and then when it dries fill the body up with baking soda and let it sit for a couple days and then clean it out and put it back together.  That would be extreme, and I don't know what it might do to the sound.  Any time you take the instrument apart that far, it will likely sound a bit different when it is put back together.  But I'd bet that would work.

So before anything like that.. First thing I'd try myself is air.  Set the instrument in front of a fan for a day or more and see if the air flow can clear out the stench.  Might even consider hanging it outdoors if you have a safe and shady place to do that where it won't get rained on, stolen, or hijacked by racoons or possums intent on throwing themselves a jamboree or something.  Might take a few days or a few weeks, and the smell still might come back to haunt you, I don't know. 

I'd also check the case.  Just the way vomit usually works, I'd suspect the case might be what actually got hit.  A lot easier to vomit into a case than F-holes, I'd think.  Case lining can look clean, but still smell foul.  On the case you could use all the usual sprays like Febreeze or OdoBan on, or carpet cleaner or whatever.

But even if the case was the actual culprit, being stored in the case would have gotten some of the smell into the wood of the viola. 

And we come to the craziest possible solution.  The main chemical that gives vomit it's distinctive smell is butyric acid.  Pernicious stuff.  Even a drop of it on a saucer will stink up a whole chem lab in a little while.  My chem teacher back in high-school did that demo.  But.. It can be reacted with another chemical to produce a chemical called ethyl butyrate.  Ethyl butyrate has a fruity smell, and is often used as an artificial flavour or scent where they want stuff to smell like fruit.  "Tropical" fruit, mostly, it smells a bit like pineapple. 

Here's where it gets crazy.  The chemical it needs to react with to do that is.. ethanol.  Booze.  It wouldn't be good to pour proof alcohol into a wooden musical instrument.  But alcohol vapour mixed with air *probably* would get into the wood as well to some degree to react with the butryic acid trapped in the wood fibers.  An old aquarium air pump with a hose going into a jar where it could bubble below the surface of some proof spirits and where another hose up near the top could take off the vapor but not the liquid itself would give a stream of ethanol vapor (mixed with quite a lot of air).  Pipe that into one f-hole so it could circulate around the wood inside the instrument and go out the other sound-hole and in a few hours it might be enough to change the smell stuck in the instrument from "barfy" to "fruity". 

The downside to that idea, is I'm not sure that "artificial pineapple" is actually a better smell.  But the upside is that ethyl butyrate is a lot more volatile than butyric acid, and should dissipate sooner.  Butryric acid (puke scent) isn't really volatile at all, and if it stays in the instrument, the smell could last a century or more for all I know.  It only needs to release a few molecules into the air to be enough to smell like vomit.  Even more pernicious than cat urine. 

Anyway, I told you it was a crazy idea.

To recap, I'd try just air first, in hopes that maybe not too much of the vomit smell is actually in the instrument and just airing it out will do the trick.  Next I'd probably try the alcohol vapor idea.  If that didn't work either, I'd take the top off and use at least baking soda to cover (or fill) the body and then dump/brush and vacuum it all out and put the instrument back together.

Oh, and take the baseball bat and go visit whoever sold you the instrument without mentioning it's distinctive aroma..

(Edited to correct a chemical name)