If you can get access from below (but you have a carpet so can't access from above) try getting someone to stand on the treads whilst you work out exactly which pieces of wood are binding on one another. Then using screws (not nails) and a good dose of PVA glue, try forcing screwsinto the various panels where the noises come from. You may have to cut some additional wedged shaped pieces of wood to force into gaps - glue and screw them in as well. Beware putting screws where they might come through to the top-side.