Oak Ply would probably be just fine.
But I think it's more expensive than birch. And isn't it harder to work with.
MDF doesn't really sound better than ply, but it is cheaper and easier to machine, paint, and more common.
Ply takes more work, but is very durable and more stiff.
I'm not familiar with the properties of Oak Ply, but if that's the material you have available I'm sure it would be fine with proper treatment of the box.
Solid wood would not be good because it resonates. Resonance is a concern with any speaker design. In a perfect world one would treat the cabinet with 8lb rock wool and use drivers capable of extending low in such an environment, but we don't live there. So you must live with what you have.
I suggest you use MDF unless you are good at wood working. Birch Ply can take some tricks to use. Such as taping the cut line. Moving quickly through the cut. Using a Good blade.