What does the term mean and what is the best way to use it? And, I also wanted to know if there is any information about where it comes from. And by the way, how do we pronounce it?
It’s an onomatopoeic term for an explosion or perhaps something collapsing in an horrendous cascade of messiness.
Things were going well until lunch, and then a bunch of error reports made my whole day go kerplewy. [My day got messed up badly].
The children’s room is kerplewy. [The room is such a mess that explosions are referenced as hyperbole].
It use is normally half-joking, certainly informal.
A variant is kablooie as in "Horrendous Space Kablooie", a term used in a comic for the Big Bang that some scientists prefer. Mostly because they have a sense of humour, but also because "Big Bang" was coined to ridicule the theory, not to name it.