Ok, this in not from experience but just postulation...I'm assuming all the baseboards are off already and you have inspected the drywall and none of it was damaged or got wet. Because if it did soak any water, the risk for for mold goes way up.
Anyway, on to the floor part. Has it been cleaned with bleach? You probably could google for the proper concentration, this would be best if you need to kill germs and any possible mold. I'm guessing you could use an enzymatic cleaner (Biokleen Bac-out or similar product??) if smell is the only issue.
Mind you, this is a theory!
So what I'd try is to mop the whole floor (pretty sopping wet, not rung out) to get it all wet and covered with the solution (bleach or enzyme) you choose. Then use a wet/dry vac to suck up as much standing water/moisture as you can, then put in a bunch of fans (maybe even a dehimidfier if you have one) and blow them all over until the floor is BONE DRY, might take a day or two, or it might take almost a week, depends on how much the floor soaks in and how humid your house is. Then procede with painting. If you are using a low voc paint and not regular floor paint, maybe go with something with a higher gloss so the finish is less permeable/harder?
A lot of work. Kilz is faster, becuase you don't have to treat as much underneath because the kilz seals in anything thats there, and makes it close to anerobic.
Follow Mothering