Is it illegal to move someones traps?

It's legal if the traps are on land owned or rented by you or your family, in which case you could even take the traps and resell them. On public land you could move them if they are a hazard to you or your family, but it still counts as the trap owner's property. If the traps are on someone else's land entirely, it's at the discretion of the property owner.