Just as there are so-called rough synonyms for 食べる{たべる}, namely, 食う{くう}, 食らう{くらう} and 食む{はむ}, to represent eating with different nuance, are there any known variants of 飲む{のむ} for drinking?
2 Answers
You can use 食らう with drinks (usually alcohol), too.
食らう
1 「食べる」「飲む」のぞんざいな言い方。「大飯 (おおめし) を―・う」「大酒を―・う」
But note that 食らう is a relatively uncommon word usually used to emphasize one's vulgarity or laziness. 食う is much more common in daily conversations of ordinary people, but I think there is no equivalent of 食う for drinking.
I've listed a few possibilities with their sources below:
杯をほす to drink (used idiomatically as 'to drain the cup') [三省堂 スーパー大辞林]
飲みほす to drink up (三省堂 スーパー大辞林)
いただく to humbly receive a beverage (although of course the meaning is not specifically 'drink')
食らう can be used for drinks too, as naruto pointed out in his post
喫する to eat, to drink (EDICT)
喫す to eat, to drink (EDICT)
召し上がる can also be used for beverages, ie お酒を召し上がる
Another possibility would be to use a mimetic word such as ぐびぐび:
酒をぐびぐび(と)やる (kotobank)
There are probably more possibilities too, if you include idiomatic phrases. I would add that the examples above don't strike me as very common usages, with the exceptions of いただく and 召し上がる, which are not strictly speaking what you were looking for. But hopefully that helps anyway.