Should I level the subfloor before or after adding another layer of subfloor?
Since you are after subfloor strength I think you'd want to level after you put the other layer down.  I assume you are gluing and screwing the 2nd layer to the first.

TCNA typically wants 1 1/4" thick subfloor.  After you install your 3/8" ply do you meet this thickness?  

This sounds like a bathroom how big is it?  Are your floor joists sized for L360?  How large is the area that dips 1/4"?