As others have mentioned, prime and paint the floor beneath the lino or carpet. A lot of what is thought of as musty smell is really the stink of old raw fir plywood. The smell gets stronger as the temperature goes up, as the wood is always off-gassing when it's warm. Every bit of raw wood should be finished in paint or urethane. It's helped in my trailer a lot.
As a side note, the main floor (2200 ft) of my house was done in birch flooring (sanded and finished in place) in 1998. Even with several top coats of urethane, birch has enough residual odour from the unfinished edges and bottoms that it is very strong when I come home after work and the house has been closed up on a warm day. It almost smells like a sawmill (not pleasant), and I have to open up the house right away.
A couple of years ago, I was camping with out-of-town friends as we toured some of BC, and at the end of the trip, they came back to my place for a couple of days. It was hot in July and the house had been closed up (no a/c) for two weeks. Within a few hours of being at my home, my buddy's wife began to cough repeatedly. They went home and a week later she still had the persisent cough and airway restriction. She went to the doc, and ended up having allergy tests done. Turns out, the only reaction she had was to birch.
When I visited with them some months later, she told me this and she couldn't figure out where she would have been exposed to birch...the light bulb went on in my head, and I told her that I had a couple thousand square feet of off-gassing birch flooring! I didn't live that down for a long time. I've had allergy problems (chronic nasal inflammation) for the last nine years (no pets, no carpet, no smoking), so when I sell the house soon, it'll be interesting to see what happens to my symptoms...maybe I'll be able to breathe through the night again!
So, my long-winded post is all about dealing with the wood. Good luck!