had a similar problem. One difference was the linoleum was glued down. The problem is that water can't evaporate up through the linoleum, nor down because the plywood is coated with fiberglass resin.
So I removed all the vinyl linoleum, then painted the floor with a gray latex floor paint
. We kept it this way for a couple of years, fixed all the leaking rivets window and door frames. I replaced any plywood areas that were still soft and repaired a damaged wheel well, then sanded the floor well with coarse sand paper and coated it with 6 coats of Spar Urethane over several weeks sanding between each coat. This sealed it well, filling all the plywood grain pores. All plywood smell was also eliminated.
Then I installed Allure (tm) flooring in an Oak print.
For myself, I would have just gone with a painted floor, perhaps a gray floor enamel, then used small rugs where desired. However, the oak Allure really dresses things up and is easy to maintain. I was reluctant to go back to a system that could trap moisture, though. But so far -- so good.