Pink Elekks are connected with the Brewfest event and were a quest objective of  and  during Brewfest 2007. The quests are in hiatus for Brewfest 2008.
Per these two quest, the pink elekks were visible in the beer garden celebrations outside of most of the major cities: "Visit the beer gardens outside of Stormwind, Darnassus, and the Exodar, zap three elekks at each location" (Alliance) and "Visit the beer gardens outside of Silvermoon, Thunder Bluff, and the Undercity, zap three elekks at each location" (Horde). However, though the quests to "disperse" them have been removed, the pink elekks were not removed and are still visible in their Brewfest 2007 locations just as the Wild Wolpertingers are still around, although the quests to catch them are also in hiatus.
Seeing pink elekks when you are drunk is a reference to the expression, 'seeing pink elephants', a euphemism for drunken hallucinations. The expression was an inspiration for the Pink Elephants on Parade musical segment in the Disney movie Dumbo wherein the eponymous elephant accidentally gets drunk and hallucinates seeing pink elephants; you might assume that many players will catch the connection to Disney rather than Jack London.