Strange boxes are a random event. A mysterious old man will appear out of nowhere and randomly give you one.
The only way to get rid of the strange box is to open it and answer the question it gives you. If you get the answer wrong or do not pay attention to the strange box, it will duplicate in your inventory.
After the last box is opened, you will get a random item from it. It could be a few coins, or a gem. The best item I ever got from one was a half key(members only).
The universe is mine and all shall bow before the might of Megafrost, master of Orion, master of the universe...