General tips for moving chests - if you just want to scooch them a few spaces you can hit them with the pickaxe - they'll "jump" away from the direction you hit them from (although they can sometimes jump to places you don't want if there's something else in the way, so it's worth being a bit careful).
However, to move them into a shed you'll just have to pick them up, and that means emptying them of their contents first - you can't pick up a chest that has anything inside of it. Once it's empty, a hit with the pickaxe will pick it up and put it into your inventory.