I'm not sure if your comment about the dynamite is serious or not, but I would not recommend that option.
You can do it with the crowbar and hammer. You may want an assortment of crowbars and hammers, especially longer-handled crowbars and some with different angles.
Another option (if you'll consider power tools) would be either a cutoff saw or chainsaw with demolition blade/chain. These types of blades/chains are designed to cut through wood with embedded nails. For such a small shed, even a reciprocating with a blade for wood with embedded nails should suffice.
U.S. Navy photo by Mass Communication Specialist 3rd Class David A. Cox [Public domain]
Ebear422 at English Wikipedia [Public domain]
Junglecat [Public domain]