Translation:The girl drinks neither beer nor coffee.
For more than two things, does one say;
"Het meisje drinkt noch bier, water noch koffie." of "Het meisje drinkt noch bier noch water noch koffie."
Based on the other "noch" example in this lesson, would this also work as "het meisje drinkt bier noch koffie"?
Yes you can say that. As a matter of fact that is a more common way to say it. ( i'm dutch, and in daily conversation the word noch is not been used very often. It is correctly, but a bit uncommon nowadays) In daily life people would say "het meisje drinkt geen bier en geen koffie". That is more common.
General consensus is that neither is paired with nor and either is paired with or. Hence in standalone sentences it is best to stick to that.
It's correct, though it sounds as if you added "nor coffee" as an afterthought.
what is the difference between noch(sounds like German) and nog(dutch) when to use one or the other?
Because that is not correct English: http://dictionary.cambridge.org/grammar/british-grammar/questions-and-negative-sentences/neither-neither-nor-and-not-either
You can use not and neither, though only when there is a separate clause (which is not the case in this sentence).
When to use Noch or nog they seem to be sinonimous but one is German and the other Dutch
why is this wrong: "The girl neither drinks beer nor coffee " and this right: "The girl doesn't drink beer or coffee." ???
"The girl neither drinks beer nor coffee" isn't correct English because you're pairing "drinks beer" with "coffee", rather than "beer" with "coffee". They need to be the same parts of speech or parts of a sentence. So you could have "The girl neither drinks beer nor pours coffee" or "the girl drinks neither beer nor coffee". Can you see the difference? It's a common mistake that many native speakers make.
I'm guessing the second is correct because it means essentially the same thing as the more literal translation and is correct English.
I disagree in that, once the general population adopts a manner of speaking, it becomes part of the language. There is an implied "drinks coffee". Perhaps don't write the sentence that way on a college paper, but there is no real ambiguity in what people would assume you mean. Also it may sound less correct outside the USA.