You can even take it to the next level:
Nem akarok semmit. - I do not want anything - Literally: I do not want nothing.
Nem akarok semmit sem. - I can only say this literally: I do not want nothing, neither.
It is not necessarily a more emphasized version. I think they are more or less interchangeable. So it would be:
Nem akarok semmit (sem).
The either part in that suggests that there are multiple people and we are answering if we want something and then when it gets to me then I just say that like the one before me, I also do not want anything. So in that regard I would rather translate that to "Én sem akarok semmit sem."
Maybe easier to look at it this way:
A: Do you want some water?
B: No, thanks, I do not want anything. "Nem, köszönöm, nem akarok semmit."
A: Maybe some apple juice or orange juice ?
B: No, i do not want anything (at all). "Nem, nem akarok semmit sem."
Though I have to admit that I would translate the "at all" differently, but maybe for an example it is good enough. Long story short, you are presented with multiple choices, not just one, and you indicate that you want neither of those and in general nothing at all.
It's incorrect English. In English, the adverbs of frequency, such as "never" generally appear before the verb but they come after auxiliary verbs and also the verb "to be", even when it's not being used as an auxiliary.
I never eat.
I never have time.
I have never eaten. (Comes after have as an auxiliary)
I will never eat.
I will never be eaten. (Only after one auxiliary verb)
I am never late. ("Am" is not an auxiliary here, but it functions like one.)
The thing is, making mistakes in English is not because any of us would be "lazy to English". It's because it takes a lot more concentration to translate from a foreign language, into another foreign language. That we don't use by choice, we use it exactly because we have no choice. So maybe... it's really just annoying when I know the word right in my language but I make a dumb mistake at mapping it to English because I'm mentally tired for that.
Well I, as a native (British) English speaker, accept that, whatever cleversome non-native speakers may tell you, you are indeed here to learn Hungarian; learning English has its own courses. By the way, though, it's 'make (not do) a grammatical error'. Also, I think you meant 'conjugations,' rather than 'cases' unless you were thinking of 'instances', but I understood your gist. (And, I made up the word 'cleversome'; it doesn't exist but I think ought to, to express 'would-be clever'.)
I've used both: Soha nem vagyok kint. and Nem vagyok kint soha.. Although, each have a slightly different meaning based word order placing a greater emphasis on the first word. The difference is subtle, however noticeable. Someone please correct me if I'm wrong :D I would love a native to chime in here? Thanks!
That would be 'Nem, nem vagyok kint soha'. There is not that extra 'nem' for the 'No'. So literally, it's just "I am never outside'. It conveys the same meaning alright, but there is a slight difference in nuance between 'No, I am never X' and just 'I am never X', isnt't there?