未 / 无 / 勿 / 非 / 没 (negation)

[盲人瞎馬]

How to differ between all those characters that mean "not have" like 未, 无, 勿, 非 and 没? 非请勿入 means something like "You won't come if you're not invited (no invitation, no entry), but how different would it be if were "勿请非入"? Or "没(有)请未入"? Or any other combination? Are they all interchangeable?

 

[ktdd]

They are not interchangeable.
There are two sets of words, one to negate a noun, one to negate a verb. And there are different nuances. 非 is negative copula, used to define something as 'is not...'; 无 is negative existential, 'there is no..., has no...'; 未 is used to mark the imperfect aspect, 'has not ...ed'; 勿 is used to give negative command, 'do not...'
非请勿入 = Do not enter if you are not invited.
无烟区。请勿吸烟 = Smoke free area. Please do not smoke.
未经授权不得转载 = Must not reprint without being authorized.

 

[盲人瞎馬]

You're great at explaining things. Thanks. Also, what is the level of formality for 勿 ? Can you use it colloquially? Is it more like Buyao or Bie?

 

[ktdd]

what is the level of formality for 勿 ? Can you use it colloquially? Is it more like Buyao or Bie?

It is ultra formal. It belongs to Classical Chinese. It usually appears in fixed phrases such as 己所不欲勿施于人, or utterances modeled on classical language such as 勿忘国耻, or public signs in the form of 请勿XX.