I've seen some people lay strand on their sides and coil/curl them up and place in a tub(s), separating each layer/string with a piece of cardboard or similar.
Others lay the strips flat and suspend from ceiling of garage.
Might depend on what material you are using for your strings in the first place.
I just do a messy job of the first suggestion, and regret it each November!
I put mine in some garbage bins. Easy to lay in there, and not too heavy to lift. They were just some Aussie made ones. I also put all my extension cables in one too, help to keep the rolled, and not tangled and snagged on eachother.