I would actually say it's wrong to say "the staff drink the beer" just as it's wrong to say "the group go there" instead of "the group goes there". The word itself refers to a bunch of people but the word is singular. This is common in English and if Danish does not have some weird exception in this case it should follow the same rule.
Collective nouns are weird. In this case, neither "the staff drinks" or "the staff drink" are wrong. One is just more common than the other. Which one is more common, depends on the dialect of English you use.
In American English, "the staff drinks" is more common (making it sound more 'natural'). In British English, the opposite is true, with "the staff drink" being more common.
For both dialects, both versions are grammatically correct, and both have been in use for at least a century.
Source (play around with it, you can even compare AE vs BE): https://books.google.com/ngrams/graph?content=our+staff+is%2Cour+staff+are&year_start=1900&year_end=2008&corpus=17&smoothing=3&share=&direct_url=t1%3B%2Cour%20staff%20is%3B%2Cc0%3B.t1%3B%2Cour%20staff%20are%3B%2Cc0
I'm sorry to diverge from the group, and especially at this point, but the final t in some words keeps sounding to me like an "l". I'm sure I must be mistaken, but since that is pretty much true for the "d" am I just hearing wrong, or is the final "t" sometimes pronounced almost like an "l" or am I merely hearing it wrong as I suspect?
The english sentence implies that more than one person is drinking beer. Is this the case in the danish "et personal/personalet", too? Is this like "das Personal" in german which means a couple of workers and cannot be put in plural (there is no "die Personals"). Is there no personaler/personalerne?
The English "staff", the Danish personale (the base form ends with 'e') and the German "Personal" describe the same thing - a group of employees
enjoying a beer together working at a single company or at a single event.
And you can pluralise it in any of the three languages. It might be a bit rare/awkward, but you can legitimately form the words "the staffs", personalerne, and "die Personale", respectively. This refers to multiple groups of employees at different companies or events.