Your book is categorically not fiction. What is it?

I'm currently in the process of drafting query letters, but I'm having a genre problem.

I've written an extensive collection of limericks on mental and social health. I know it's not fiction. It's closer to non-fiction, but submission instructions for non-fiction often ask for sample chapters, and this collection won't be in chapter format.

Ok, fine, it's a poetry book, but... I think of poetry as relatively esoteric stuff, and I don't see this book belonging in the poetry section. I think it makes more sense to present it as a kind of humorous self-help book, or a novelty book one buys near the cash register at Urban Outfitters.

Thanks for any guidance you can offer on creating an appropriate and effective query letter. 

You're closest with "novelty book" but the correct term is gift book.
You query this as you would non-fiction, and while it's true you don't have sample chapters, you have sample pages. You'd include some of the limericks.

Were this to cross my desk the first thing I'd look for is platform. This is the kind of book that needs 10,000+ Instagram followers to be viable.

Also, I don't know what "social health" means.

The trick to getting category right is find books that are like yours.  Look at the back cover. Often there will be a category listed for the book.

This is the back cover of Life's Little Instruction Book which is a gift book, and also considered self-help.  Most books have this kind of information somewhere on the back cover.

Here's are some other examples from three books pulled at random from my shelf:

Lower center

Upper Left corner

Upper left corner