I'm with Kirk on this one. I wouldn't worry about wood crates. Museums routinely use unsealed wood boxes, either plywood or OSB, for shipping and, if necessary, storing artwork. I had to make four shipping crates for my last exhibit, which traveled to 10 different galleries/museums over the past year and a half and, when I get them back in February, I'll be using the crates for storage.
What I would not use, under any circumstances, is exterior-grade sheet stock (green or brown treated) as, unlike interior plywood or OSB, they're usually sold "wet", and will give off a lot of chemical evaporation.
As for storing inside plastic bags to protect against moisture that may permeate the wood...unless those bags are hermetically sealed, they won't do much good as any humidity will find it's way to the artwork. However, if you have to worry about the crates getting wet, they you really need to think of another location.