Get a few cans of compressed air and remove as much of the particulate as you possibly can. After that it just requires a lot of time with alcohol and various ways (cloth/paper towels, Q-tips, magic erasers, etc.) to apply it in order lift away the remaining tobacco-stuff. The places with the air circulation are what you want to pay the most attention to, because even a little bit of that stuff left in the path air takes inside can be really foul. I have no experience with motherboard washing, but that might be something to consider if it's just caked in there.

I'm not sure how you would get all of the moisture out of the keyboard if you washed it without disassembly. Try a magic eraser and alcohol, being careful to let all of the gunk drain down and out before resorting to the dishwasher.