I mentally file all of my artwork into two crudely-labeled piles: the Kind That Makes Sense, and the Kind That Does Not Make Sense. Generally speaking, the Kind That Does Not Make Sense is more fun, though it often arrives by accident when I'm aiming for the making-sense-type of art. Here are a few recent examples.
Below, I was trying to draw what I can only describe as a “pile of crap” for another cartoon (long story), and this is what wound up happening.
Below is a drawing I started at a restaurant a few months back. I was doodling the guy at the table across from me, and it all snowballed from there:
Here is me having fun with heads in profile, and a new slant-angled Micron pen:
It took me awhile to realize that there's a sweet spot with weirdness in art: too strange, and it becomes off-putting, and too normal and well, what's the point? You have to be unusual, but still give the viewer something to cling onto. Being weird can also be used to disguise a lack of ideas, or talent (see how many artist statements abandon explanations in the first place, and just spout gibberish as a means of distractions).