Is this word formal? I've never heard it in speech. It's always "in no way".
I would say it is really informal. Perhaps it's colloquial to a specific dialect, you'll need to wait for US speakers to say so, but it's definately a US term.
I've heard it in films/programmes to emphasise, e.g.
"There's no way I'm going in that cave. No way and nohow."
At least, I think this is the right word? I would have thought it was 'no how' - two words.