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For the stronges stairs you have ever seen use plywood. Take 3 pieces of 3/4 and rip them in half lengthwise so you have 6 pieces 2' by 8'. Cut one of these in half. Lay two of the full length pieces end to end, cover them with subfloor adhesive or weldbond (good glue) lay a 4' by 2' piece at the end and an 8'piece in the middle and the other 4' pece at the other end so that the joints are offset by 4'. More glue. Lay on the other 2 8' pieces then screw thae crap out of the whole thing, flip it over and apply more screws from the other side. YOu will now have a glue lamb beam that is 2.25 inches thick and strong as hell. Now it gets tricky lay out your stairs so that when you make the cut you will end up with 2 stringers out of one cut. With a little forsight and planning it is not that hard but you gotta think before you cut. You will end up with seriously beefy stringers with no bounce. Even if your 400 pound mother in law comes over and falls down the stairs they will not bounce.
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