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2.
When you invoke Odin's Beard you shout "I invoke Odin's Beard!" out of sheer frustration at a situation you can do little to nothing to solve. You then refuse to shave until said situation is resolved. The longer the problem is unsolved, the longer your beard gets. In some cases you end up not shaving for months, even years, thereby growing a beard rivalling mighty Odin
Often used to simply make girlfriends or wives do what you want, lest they suffer the bristly wrath of your unshaven face.
Odin's Beard can also be used by females, either as a satirical jibe about their lack of facial hair, or in referance to pubic hair (once again, to annoy their significant other in order to manipulate them)

Odin is well known for his spectacular beard, providing a stiff competition for his son's beard, who was Thor
Colonel Gaddafi is pissing me off! I invoke Odin's Beard until someone ousts that motherfucker!
by Sethkasketch2 July 15, 2011
 
1.
The hairy growth on the Norse All-Father's chin.

Used as an exclamation of surprise.
By Odin's beard!
by Dann Woolf June 15, 2009