KnowYourPhrase.com - The Meanings and History For Popular Idioms and Phrases
Sheds are most often located somewhere in a person's backyard, and are used to store belongings. A common thing to find in sheds are tools of various kinds, some being sharp, others blunt.

This phrase looks to be a very recent one. The earliest I could find this expression in writing, for example, is from the Colorado Springs Gazette Telegraph, July 1994, where it reads:

    "Critics said that Cliburn was an intuitive artist, and that once his intuition was exhausted, he had little 
     else to say about a piece — which was a fancy way of saying that Cliburn wasn't the sharpest tool in 
     the shed."
* When it comes to cooking, I'm not exactly the sharpest tool in the shed, so I keep my meals basic most of the time. They still taste good, though!

* My orange cat is not the sharpest tool in the shed, but that's okay, he's still adorable!
Note: The origins for many popular expressions are unclear. In these cases, what may be provided instead is a theory as to how a phrase may have originated. If no theory is given, then I'll try to at least include a quote on the page to give you an idea for a old a phrase is, at minimum.

Moreover, quotes that contain a phrase may be taken from old newspapers, poems, or books that were written centuries ago. If I quote a book from 1650 because it uses an expression, that does not necessarily mean the expression originates from this book. It simply means the saying is at least that old.

N-Letter Sayings  |  Know Your Phrase - The Meanings and Origins For Phrases and Common Idioms
N-Letter Sayings
Meaning:
Origins:
Example Sentences:
Phrases and Idioms
A hand tool called a saw. Be careful, it's sharp!
Someone who is thought to be unintelligent; stupid.