Hoch HIvje' Hoch HIq vItlhutlh. I drink all the ales in all the goblets. Does this mean there are several kinds of ales?
HIvje' HIq naQ vItlhutlh. I drink the whole ale of the goblet. Does this work to signify the whole amount of the ale?
Are there other ways to express drinking the entire amount of ale in one or more goblets?
Does naQ work with liquids?
For what you are trying to say, I believe you need to break it out into multiple sentences. Something like:
Hoch HIq vItlhutlh. raSDaq Hoch HIvje' vItebHa'.
I drink all the ale in all the mugs on the table
(Lit: I drink all the alcohol. I drain each mug on the table)
"Does this mean there are several kinds of ales?" – The sentence makes no mention of "kinds" so there's no information in it to tell you anything about what kind of ale is being drunk.
HIvje' HIq naQ vItlhutlh means "I drink a complete mug beer". I don't believe HIvje' HIq means "a mug of beer". It would seem to mean "mug beer".
I believe you are too focused on the English expression "a mug of beer" and instead should focus on describing what is happening using Klingon words and multiple sentences.
In Conversational Klingon, Okrand says the following lines:
romuluS HIq vItlhutlh. – I will drink Romulan Ale
HIvje' tIn yIteb. – Fill a large glass
If Klingons had a simple way to say "I will drink a large glass of Romulan Ale" then I would have expected it to be used here. Instead Okrand used two sentences to say what, in English, would have been one.
Ah, now I'll have to work on how to say a mug of beer.
I feel like I have reverted to taghwI' level of understanding this language.