This is a hilarious idea and I love it. You could have Dude or Al Fabet act as junk traders (even more than the actual junk traders in Junkyard) that take in the most random crap ever for nonsense reasons. I can totally see Dude saying something like, "I need 40 sledgehammer handles and 56 flares, stat! The tiny aliens in my Mushroom Brew demand it, and they're not messing around!"
I know that the rags and bottles are useful as molotov components, so maybe the Free Drones could accept them?
I got in mind that Fallout 2 quest when barman in Vault City asks you to bring real alchohol.
And yeah, Dude seems to be a perfect candidate for it, just imagine - you can't sell 4-5 items in the game, and boom! you finally have found a weirdo that needs exactly that in large amounts, with no real money in return, just some funny fluffy dialogs. Or something like that. Or different.