Well, the good news is that you have a pier and beam foundation, and the worst of the damage appears to be with the house's original hardwood flooring. The bad news is, the subfloor is going to require repair, and you likely have drywall damage in that closet.

What I'd do is, while it's still damp, try to ascertain how far up the wall the moisture has crawled. You will need to cut the drywall out from about an inch higher to insure that you don't have any nasties growing in the wall to insure an even bigger mess down the road. All you have to do there is then replace the cut out material with new, and then tape and mud the seam. Since the closet is small, you may be able to beg off some excess material from a nearby construction project. While the rough in is exposed, I'd paint a good thick layer of Kilz paint to halt any mold growth behind the walls. As for the hardwood floor, I'd just cut it out of the closet, and replace the floor in there with some sort of metal catch pan with a french drain to avoid a repeat. If you have carpet, anything damaged beyond the closet floor will need to be replaced with 3/4" plywood to fill the resulting gap.

With the subfloor, I'd at least seek the advice of a professional as to the best means of it's repair. It just may end up bieng one part of the job that would be better suited for the pros.