1. You can't buy alcohol until you are twenty years old.
2. You can't buy drinks until you are twenty years old.
3. You can't buy wine until you are twenty years old.
4. You can't buy beeer until you are twenty years old.
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Are they all grammatical? Which one is the correct term which is used in general?
All are correct, except for the typo -- beer (2 e's!).
The one used in general is #1.
All of the sentences you provided are grammatically correct. However, there is a slight error in the spelling of "beer" in the fourth sentence.
In terms of which term is used in general, it depends on the context and the specific regulations or laws in a particular region. Generally, the term "alcohol" is more commonly used to refer to any alcoholic beverages, including wine and beer. However, different countries and jurisdictions may have their own specific legal drinking age and terminology, so it is important to consider the specific context in which these sentences are being used.