Are nails okay for flooring the attic

4 inch thick insulation is thicker than a 2x4 (only 3.5" thick), which means you'll be compressing the insulation and decreasing the R value. Instead, I'd suggest laying the new insulation on top of the old (no need to throw out the old unless it's turned moldy), without a vapor barrier on the new (you only want one vapor barrier, against the ceiling), and going perpendicular (to the old to reduce the air gaps).

With 2x4 joists, I'd suggest that they are not load bearing and I'd recommend against putting any further load on top of them.

Since you are in zone 4, R-38 is a reasonable insulation level. That doesn't tell us how much an issue a lack of vapor barrier is. It is less of an issue in dry climates. What a barrier does for you is prevent moisture from condensing inside the insulation, significantly reducing it's insulating value. Ever notice how hypothermia victims have invariably gotten themselves wet? Unfortunately, properly installing one can be very difficult (read: expensive). As it happens, plywood acts somewhat as a barrier, depending on it's construction. Thus, you may need to just focus on gaps and openings.

Another possible make-do vapor barrier is a good heavy coating of latex paint on the ceiling. You may already have this! Truth be told, the best way to insulate would be to remove the plywood and blow in the needed insulation. This gets sealed around all the joists and other ins and outs nicely and makes effective use of what little insulation is already there. However, it may not be worth the effort.

You can still get a good insulation job by layering it on top as you suggest. The draw back is the dead space under the plywood effectively becomes part of your conditioned space, greatly diminishing the value of what's there. Even a plaster ceiling alone is worth something. And you've increased the top story volume you're heating 5-6%. Another issue with this approach is the plywood becomes your vapor barrier. What are the ramifications of moisture condensing on the under side? There's poor air circulation, so it will not dry easily. It could be the cause of a mold colony gaining a foothold, which can have serious health consequences. Or it may not be an issue if you're in a dry climate.

Whichever way you go, try to ensure what ever passes as a vapor barrier is a complete as possible. Ensure any recessed light fixtures are not insulated over, and that no insulation contacts the cans. It may seem more efficient to cover them, but you greatly increase the chance of them overheating and starting a fire. Insulation is little good if your house burns down! A truly efficient ceiling has no recessed light fixtures for this very reason. Note that there are supposedly fixtures rated to be covered, but I don't think I've ever seen one.