I had to completely remove the interior of my Neon a few months ago due to the dang taillight seal problem. I had water about an inch above the carpet on the right side of the car all the way to the front of the car, along with the spare wheel well filled 1/2 way up with water. Ended up driving around for a few days with the dash and a driver seat, lol. No other seats, no carpet, no console, nothing in the trunk...
I did get the carpet and rear seat cushion completely dry using a circulating floor heater. Inside floor pan was dried with a shop vac. The padding on the bottom of the carpet was thoroughly sprayed down with Lysol. It got rid of that smell (moldy, damp, wet-dog-like smell) and it has been fine since. Gave me a great chance to completely clean everything to which is always nice IMO. Being an OCD detailer will do that to you, lol.