Wow, I feel really bad for all of you that had rough experiences with being caught. I guess I just got lucky. I know my parents found my stash at least once (probably more), but they never confronted me about it.
My step-dad used to like snooping through my room (looking for drugs and whatnot), and apparently took pictures of anything he found to show my mom. I came home from work one night, and she said that he had showed her some pictures of what he found: certain things that I had thought I hid better and (her words) "some things I don't understand". She just told me to choose my hiding spots a little better, and left it at that. Never brought up the diapers. I picked a new stash spot (I had been keeping them in an old PS3 box at the bottom of my closet), and started periodically moving them around. That was when I was in the binge/purge cycle, though, so I rarely had diapers in my room for extended periods of time.
There was another time that I had ordered a sample diaper, and it came in a large manila envelope. They must have seen me pull it from the mailbox, and then questioned me about it when I didn't bring it inside (I stashed it in the garage to retrieve later). My step-dad made me grab it and show it to him, and I stuttered out some explanation about kids in my class playing pranks like this. I doubt they bought the story, but, again, nothing was ever said about it. I'm assuming it made them pretty uncomfortable (my family has never been the best with communication), so they tried to just ignore it.