Locations of the crates:

Where you find the axe.
Where you began the game.
Four inside the hut.
With the teddy bear, after crossing the bridge.

The axe is broken after smashing the crates that are necessary to the story (where you find the axe, where you began the game and the one with the teddy bear), so make sure to break everything before smashing the one with the teddy bear (I suggest you to break this one last, especially if you're also doing Murderer, involving the sheep that you need to kill before breaking the axe - in other words, before smashing the crate with the teddy bear).