What lumber should be used for indoor stair stringers?
In my area, they use 20' long 1-1/4" x 11-7/8" LSL for stair stringers. Creating your own stringers with plywood aren't a great idea, half of the plywood plies aren't doing anything when you use them as a beam since every other ply is turned 90 degree when stacking. If you can't find those in your area, then buy 1-3/4" x 11-7/8" LSL. If you can't find that, then buy 1-3/4" x 11-7/8" LVL. 

The only other normal option is using 2x12 stringers. They only use that for deck stairs because we can get treated southern pine 2x12s. You can't get treated LSL or LVL, so it's not an option for decks. If you're worried about warping just double up and nail and glue 2x12 stringers together. 

If you really want to build your own stair stringers, use OSB instead of plywood. The plywood will have a tendency to split at every riser, but the randomness of the strands in OSB help prevent that splitting while the stairs are deflecting under the live load. I'd say subfloor adhesive on all contact surfaces and clinched 8d or 10d nails every 6-12", but that's just a guess in the dark.