They are made of a plastic formed by combining phenyl and formaldehyde. With time, the plastic degrades into it original components. That's the smell you detect. You can't deodorize it but you can store it so the odors dissipate into the air.

Heat and light accelerate all chemical reactions so the warmer the storage environment, the faster the decomposition. The ultimate storage would probably be a freezer. An old working refrigerator would serve too.

Storage in plastic bags is not a good idea only because it traps the gasses.

Just like old dice, the plaques will eventually distort and fall apart. Give them a proper burial at the end.