How can I rebuild creaking plywood-based stairs?
You should not have to rebuild the whole staircase.  Rip up the carpet so that you can see the problem. In most cases it is caused by treads becoming loose. If this is the case I would take the treads off, put some construction adhesive down, and screw the treads back.  If you see that you have a broken riser then you may have to replace the stairs or fix the riser. Let me point out that the treads will most likely be unfinished under the carpet so you might consider either replacing the carpet or installing a bull-nosed wood tread.