Is insulation or damp proof barrier a requirement for walls in wood sheds?
Without sealing it pretty well (and it sounds like it's not right now), I don't think you'd gain any benefit from insulation. To be truly effective, you need to seal up air gaps, holes, etc. You'd also need to then consider insulating not only the walls, but the ceiling as well.
For an unconditioned space, sealing things up may just lead to other problems. If it's humid out and you're going in and out, you're letting the moist air in. Close it up, you seal it in next to your tools. Not great. Putting in something like fiberglass insulation in the walls would also make the drying of any moisture that got in the wall cavities take even longer, which is exactly what you don't want.
If you have no plans of heating/cooling this shed, and it's just an outbuilding for storage, I don't see why you'd bother with the expense and effort of insulating it.