I agree with a previous poster- DE (food grade) works WONDERS on smell and dampness! We get ALOT of rain and humidity here so it gets pretty yucky sometimes. I use shavings in the barn and henhouse, but I use DE liberally on all the ground surfaces and roosting sites. It can be smelly sometimes (I just cant always clean like I need to if its raining and the kids are home all day) and so I get a bunch of DE and pour it over the really bad places thick, and then sprinkle it over everything else. It REALLY knocks the smell out, almost immediately. I do go out and scoop out the bad spots as often as possible (after Ive added DE) and then sprinkle DE over those cleaned spots again. It also keeps flies down since there is no moist poo to land on and they dont like to walk on DE.
It is kinda expensive, but not as bad as replacing shavings once a week or building a floor in the coop and buying sand etc. You could try it as an experiment to see if it works for you before trying the other solutions offered that may be more work or expense. I do spinkle it in their run/penned area, but not alot since the area is too big for that to be cost effective, but my flock free ranges, so there isnt alot of yuck in the pen to deal with, just mud sometimes. But mud dries out eventually, so I dont worry as much about it.