can we move the neighbors shed off our property?

This is a boundary dispute. While you can move the shed, if you do it and the shed is damaged, you could be liable. Have them move it. If indeed the dog fence is on your property, the right answer for your situation is to send a polite letter. You had the boundary surveyed and the shed is on your property, please move it in a reasonable time. If too much time passes, send a second letter, less nice, saying they have x days to move it or you will file an action for trespass. If they still refuse to move it, then call a real estate lawyer. Regarding the dog fence, you can be nice or mean about it. The only question is to what extent it effects your enjoyment of the property. If it doesn't affect things at all, I always tell people be nice, you never know when you need a favor from a neighbor.  The nice way is to mention it in the letter above and say, we will lease you an easement for the dog fence on our property for $10 a year. If they agree, the fence is now leased and they cannot claim adverse possession. If you want to be mean, you can order them to move it.    Good luck!