I keep a bail of hay in the garage in a large open cardboard box up on pallets to keep it off the floor a tad.
My pellets I move from the feed bags to covered containers, more for ease of use. If you seal up the bag again it should keep fine. My pellets have a zip lock top, but I keep tipping the bag over, so I use containers and a measuring scoop.
Same with the dust.
We get sugar in nice 4Lt containers, I recycle them for feed & dust.