I have not heard "strung up"" used in this manner. I have only heard it to mean a hanging (or lynching). I have heard "strung out" which means to be under the influence of drugs, and "wound up" which means to be nervous or excited. It's possible that "strung up" is used elsewhere or that it has become obsolete to avoid confusion. "wound up" would work in sentences #1 and #2 but would not work in #3 or #4 as written 3. Stop getting (all) wound up, everything will be alright 3. Don't get (all) wound up, everything will be alright. 4. You don't have to get (all) wound up, you'll do it. 4. Don't get (all) wound up, you'll do it.

I've not heard it used that way. You'll often hear the term "he's highly strung!" meaning nervous and easily upset. https://en.oxforddictionaries.com/definition/highly_strung "I could get you strung up on a tree so easy it ain't even funny." - Quote from Of Mice and Men. In this sentence "strung up" means lynched or hung by the neck from a tree.