I got a lifetime's supply of
cardboard egg cartons at a food pantry. They get hundreds of them with a few broken eggs to pick out. They consolidate into good dozens and accumulate extra cartons.
For your situation, I'd clean them and put them in cartons in the fridge. Keep them in order so you can always give away the oldest ones. Or put them (dirty) in cartons and keep them in order, then clean and give away the oldest ones