Wood and foam sandwich = composite panel.
The wood you are describing may be Luan, a generic label for three-ply hardwood plywood, mostly from Indonesia or other Asian countries. It is used extensively in the RV industry for paneling and filon backer.
If you have extensive water damage inside the walls, you'll need to access those areas and deal with them, any rotting wood will continue to rot. The dilute bleach solution will work to kill off any fungus, i.e. wood rot, mold and mildew. I use a spray bottle and cover the surface with the solution. You could also use Lysol (Original formula with phenol) or Listerine mouthwash (again, Phenol).
When you have the floors repaired and are ready to replace the foam, buy extruded polystyrene with radiant barrier. It has twice the R value of expanded polystyrene, AKA- bead board, Styrofoam and has greater structural strength. I'd also suggest to install a vapor barrier between the foam/wall framing and the interior paneling.
Are all the walls and floor affected or just some areas?