This quest is available during the Brewfest event.
Getting drunk is a time-honored tradition at Brewfest - it's damn near required! Thing is, I'm getting reports across Azeroth saying the celebration's plagued by hallucinations! We can't have that!
These elekks can't be harmed by normal weapons - they pass right through 'em - so take this fabulous piece of Gnomish machinery, visit the other beer gardens, and zap 'em to oblivion. Remember, you have to be drunk to see 'em!
If you're at one of the beer gardens mentioned (Stormwind, Darnassus, or Exodar), and you don't see the Elekks, you aren't drunk enough. Take another drink. It take's 3 'standard alcoholic beverages' to see the elekks.
There has been some concern and issues with this quest's availability. It is a known bug that some people (mostly level 70's) can't get the quest.
Hopefully Blizzard will correct this soon.