When I had several broodies at once, I found out that hens can indeed move eggs around. I mark and date eggs when I let a hen have a clutch to hatch. That way, I know which ones belong together, if anything weird happens. With chickens, something weird happens all the time. Anyway, I check the nests daily when I have broodies, to remove new eggs other hens have laid, and to remove any broken eggs. When hens kept coming up with the wrong number of marked eggs in their nests, I checked dates, and found that one of them was stealing eggs from other nests, and putting them with hers!
I never saw them do this, but somebody else said she'd seen a hen tuck an egg under her chin and carry it off.
I had a bunch of wooden eggs once, too, and they disappeared. Later, I found some of them out in the yard, by the driveway. I don't know if she went in and got them, or if the hens tossed them out, then she found them, but my dog Cleo had taken them to play with. Dandy dog toys, those wooden eggs!