The first mistake the builders made is the 24" centers of the trusses. The only material that could span such a distance would 1" solid plywood. Builders and engineers make the mistake of building just to safely and load guidelines. And a 3/4" OSB will sure span such a distance safely but not without pops and squeaks. And that's the rub, why must we live in expensive but aesthetically inferior new building, just so builders can save 5 dollars a sheet using substandard, but known inferior materials.
But I digress. The second mistake was allowing the OSB to get soaked. But first, during the OSB manufacturing process some of the small chips of wood are bent as they are being bonded and pressed into layers. During the rain the swelling opens those bent and folded chips and when compressed for a second time by your walking on them, they finally break. If there are only a few of these fibers breaking you will only hear a slight cracking sound, but some people experience popping sounds like Rice Crispies.
The OSB manufactures say this is a manufactured-related characteristic, and they take no responsibility for this problem. Even still the Louisiana-Pacific Corporation has been saddled with multiple class action lawsuits since 1997 because of OSB panel failures.
But like I said once the fiber is finally broken, it will lay cracked but quiet. Since this material has 4 times the resin content of plywood, it also has the tendency to bend more than plywood. And the 24" centers have just added to this deflection. This is well known in the building industry, and a short visit to any plywood association web sites will confirm what I say.
Because the two major hardwood flooring associations have accepted OSB with open arms this has become the industry standard for subfloor requirements for hardwood floors. So everybody passes the buck as they line their pockets at your expense.
I can only make the following suggestions, and I would wait several years before considering this repair as the popping sound I think (and hope) will get better on its own.
At the very least you should nail down 5/8" plywood (over the OSB) hitting the joists with 4" spiral nails. I say this is the least because the hardwood flooring nails will still penetrate the OSB 1/4". But I would hope this would not cause too many squeaks in the future. And this will keep from raising the final floor level too much, so as making too high a rise to the various stair cases.
But 3/4" plywood on top of the OSB would be better, as the flooring nails will almost only contact the plywood, and be as if the OSB wasn't there at all.
And the very best thing to do is to remove all or most of this substandard building material (OSB) and replace it with 1" plywood, or even 1" by 4" Southern Yellow Pine laid diagonally to the joists. This last suggestion makes the very best nailing surface for hardwood flooring, if you've got really deep pockets.
Your 3/8" solution may not be enough. And any plywood covering the OSB should be glued on the joist line and between the joists. And urethane adhesive is best, but you may have to mist it if the wood MC is below 8%. And don't dismiss the squeakenders or sagenders solution, it may be a lot less disruptive to work under the floor than on top. You can use the sagenders to add plywood panels to the underside, thus ending the deflection.
But if you must work from the top you can use a nail spinner to spin in 3" spiral finishing nails just where you said. Nail spinners can be bought at http://www.leevalley.com, order product #99K20.01. They work a lot better and faster than preboring, I use them in all my installations and repairs.