The meaning of awe is given in dictionaries as "an emotion variously combining dread, veneration, and wonder that is inspired by authority or by the sacred or sublime" (this definition is from Merriam-Webster, the meaning in the OED is more expansive but basically the same).
Awesome, the adjective derived from the noun, means, in its old and literary sense, "full of awe" or "inspiring awe". But awesome has a colloquial and slang usage and meaning as well:
"It is one [of] the three words which make up most American sentances [sic]. The American vocabulary consists of just three words: Omygod, awesome and shit." (Urban Dictionary; similarly, though less profane, in the OED)
Does awe have a colloquial or slang usage as well? And if not, does the common colloquial use of awesome influence the meaning that native speakers of American English understand when they encounter the word awe?