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The musty odor is probably mildew. All of them "should" be washable, but to really get the odor out you'd want to wash throughly with hot water and let soak with a dose of bleach for a short while, then air dry really thoroughly.
If a cover is not removeable...there may be mold spores you won't be cleaning out, too. If there's a way to open a seam to open them up, explore the option. A professional "carpet cleaners" can usually pass the cushions (not the vinyl covered ones, but raw foam or cloth-covered foam) through a carpet/upholstery cleaning machine that will really do a good job on them--and then, make sure they are properly dried again afterwards.
Just airing won't get the crud out of the foam, which is usually open-cell and really needs a thorough washing.
Once they are back in the boat, a good way to keep them fresh is to tip them up on edge before you leave the boat, so they can "breathe" better than laying flat against the wood under them.