I do not smoke. (right now) *This statement can imply both that you don't smoke right now or in general. I do not smoke can be interpreted as 'I don't smoke now, nor have I or will I.' I cannot smoke. ( I do not want to smoke, because of my health or ...) *Saying 'I cannot smoke' implies that you can't smoke because of a reason (health, etc) whereas saying 'I don't smoke' can imply either that you don't want to or that you choose not to for a particular reason/reasons. I cannot not smoke. (I need to smoke - I am addicted to smoking- I can not discard smoking.) *Very good! Most people have problems with double negatives. Make sure you say 'not' as opposed to 'no'. I can not smoke. ( I got used to smoking but I am self control too.) *This is accurate, however you would have to put extra emphasis on *not* when speaking. However, most people wouldn't phrase it this way simply because it can cause confusion. You could say something like, I can choose not to smoke. That implies more self control than the original sentence.

"I do not/don't smoke." - This one's good. "I cannot smoke." - This one is good. "I cannot no smoke." - This should be, "I have to smoke." "I can no smoke." - This should be, "I don't have to smoke."

The first two are fine. The other two need the phrase "not smoke". ("Smoke" is still a verb here.) The third sentence is more colloquial, with its double negative... but in this case, the double negative cancels out, as you correctly interpreted. The fourth sentence is far too close to "I cannot smoke", and we should avoid it because it is unclear. Try, "I am able to not smoke" or "I can avoid smoking".

'In the situation of addiction to smoking, it would be more natural to say "I can't stop smoking"

Thank you, Kenny.