Gator Joe:
I should preface by saying that I have a degree in mechanical engineering, but have virtually no knowledge or experience in construction carpentry or framing, so take what I say with a bit of salt. I've been renovating for 20 years, but it's all been in the same apartment block where every suite was constructed the same way with the same materials, so it's probably more correct to say that I renovated the same apartment 21 times than to say I renovated 21 apartments.
Why install OSB as a subfloor? I would be concerned that if you dropped something heavy up there, it would go through the OSB, or at least leave a major dent in the OSB.
If it wuz me, I woulda gone with T&G plywood, or fir 1X6's, just like a normal sub-floor for a working floor.
That 2X4 running the length of the attic and nailed to the joists effectively acts like blocking, but so would your OSB.
Welcome to Blocking 101:
If you have a joist holding up a floor, it has the most strength when it's vertical. As you put more and more weight on that joist, then the more it bends under the weight, the more it wants to start twisting under the weight. Once the joists twists, it looses very much of it's strength. Imagine a 2X12 on it's side; it's not nearly as rigid as a 2X12 that's straight up and down. In fact, you can use a 2X12 on it's side as a pretty springy diving board. So, the more a joist twists, the less strength it has to resist bending, and the more it starts to become easy to bend like a diving board.
The purpose of blocking is simply to keep the joists vertical so that they remain most capable of resisting bending. You can do that by putting a row of solid wooden blocks between the joists at mid-span, or two rows at 1/3 and 2/3 span for longer spans. You can also do it by putting in what they call "cross bracing" between the joists and they make steel cross braces that are hinged in the middle that you just nail in rather than make from scratch like wooden cross bracing. Or in a case like this, where the joists are supporting nothing more than a drywall ceiliing (if that) and the need for blocking is minimal cuz the weight supported by the joists is minimal, you can supply some "blocking effect" by simply nailing a 2X4 along the top of the joists. That 2X4 will help prevent any one (or several) joist(s) from twisting, but it don't help much if there's so much weight on the floor that all the joists are wanting to twist cuz if they all twist in the same direction, that 2X4 will just go along for the ride. Only solid blocking or cross bracing between the joists will prevent a collapse if all the joists are wanting to twist.
You can take out that 2X4 cuz the stuff you're nailing down will do the same job.
Considering this is gonna be used as a floor from now on, and if it was me, I would buy some steel cross braces made to be used between joists and put them in in two rows; at 1/3 span and 2/3 span. That's cuz 24 feet by 24 feet is a real big floor with real long joists. Also, if it wuz me, I'd use T&G plywood subflooring cuz you're prolly never going to take the flooring out, so you may as well install something more sturdy that can serve for any purpose throughout the life of your house, and possibly more than just light storage.
But, truth be told, as long as you're only using that space for storage, you'd be fine with OSB and using the OSB to do the same thing as the 2X4 you're wanting to remove.
Can you post a picture of how those 2X12 joists tie in to the walls on each side of the garage? I'm sure the carpenters in here would want to see that detail. I'm just concerned that the builder might have done sumfin stupid like just nail the joists to the sides of the studs in those walls. You wanna be confident that the joists are resting ON those side walls so that the walls properly support the joists.
I think that horizontal 2X6 in the first picture was installed just to hold the wall vertical, and that you can replace that strut with anything else that'd hold that wall vertical. No one is going to tell you to remove that strut without providing some other means of holding the wall vertical cuz the original builder obviously saw a need for it.