Spar urethane is said to be the best sealant. I use poly because it doesn't yellow as bad, and is more forgiving to apply. Epoxy is good in my experience, but a pain to apply. I don't care for polycrylic, I've seen it bleed yellow (top of osage) when it got wet in a rainstorm, and even after my usual 5 to 7 coats. Tru oil is probably the most forgiving and easy to apply, but imho you need lots and lots of coats, say 10 to 20... fortunately w/ tru oil this is no giant burden. I wax (parafin rubbed in w/ mineral spirits) on top of of whatever, and I personally think this is as important as the finish you use. Parafin will bead water top of most anything, even by itself, and lasts plenty long as a typical wet outing.
I live in a humid climate and became very careful about moisture control after lots of projects, most of my projects, turned out with more string follow and less cast than other's I read about on the net. I use a postal scale and a hot box with several Rh gauges to monitor moisture content (or did when I was still active in the craft) and I can assure you osage does take up moisture just like every other wood. This regardless of whether it's nekkid or sealed. But it does seem to take a relatively longer to take up moisture, and or does seem to retain it's strenght and resilience better than some other species (like elm). This perhaps simply due to it's specific gravity... it's heaviness. It has so much wood in it (per volume) a particular amount of moisture counts less, as a proportion of total mass. Folks also speculate "extractives" in it's sap have an effect. Anybody who has cut osage can testify, that milky sap is some kinda sticky shiite. That's gotta count for something.