'Drunk as a skunk' is a saying - probably American, given that skunks are native to that country, and that life is so bleak over there than any release is welcomed - indicating that the subject is very drunk indeed. As drunk as a skunk, in fact.

Skunks themselves are not noted for partaking of the demo drink, and the phrase derives from the term 'stinking drunk', or 'drunk as stink', crossed with the fact that it trips of the tongue as easily and pleasantly as the words 'vulva' and 'moon'. It was probably first uttered whilst the originator was drunk. It's one of a number of similar animalistic phrases, including 'fat as a rat', 'crazy like a fox', 'hungry like the wolf' and 'happy as a lamb'.