It's possible that they are laying their eggs somewhere in the woods and/or one or more hens are hoarding them getting ready to go broody. I'd take a look around their zone. A drastic drop like that may mean hidden eggs.
Of more concern than fungus in the woods and standing water is their regular feed. Did it get wet in the heavy rains? Feed can develop mold and contaminate quickly in humid conditions if it's gotten wet. I'd double check it.
I don't think that mushrooms would be that much of a concern but you never know with chickens. However,if chickens, and most animals for that matter, have enough nutritious food to eat, they will seldom eat toxic plants. Where I live in the West we have some pretty toxic milkweed that grows in pastures and most of the animals who eat it and die do so because they lack enough good food.
I would suggest a walk about the place looking for one or more chickens sitting in a small nest under a shrub or in tall grass. Look for hidden eggs. Then I'd carefully check their feed. And chickens do on occasion just drop dead due to genetic problems and/or heart defects.
If nothing else, you could probably have a necropsy done on the dead chickens; many universities and/or agricultural extension offices have resources for this and it might not cost you anything.
However, if you have too many more die, you'll need to get the necropsy done and you may have to notify a livestock inspector and/or another authority in case there's a contagious disease going around.
Good luck and I hope things improve for you and your little chickens.
Mary
