Does America have its Versions of U- and Non-U English?
Solution 1:
Yes. The most stereotypical example is Ebonics and is a somewhat touchy subject due to the racial implication of calling African-Americans a lower class. The term seems to have officially become African American Vernacular English.
Most other examples I can think of are things like hick or valley girl. The terms are shifty and ill-defined because of the nastiness implied by the overarching terms. But each of those examples have their own vocabulary, mannerisms and idioms.
The Ivy League also has a stereotype associated with their speech but as far as I know it is nothing worth studying beyond humor or general classism.
(By the way, I apologize for all of the Wikipedia links. I am hoping this spawns a few interesting paths through the web.)
Solution 2:
Depends what you are asking.
U speak in English was a parody/attack on the bourgeois middle classes for using clever or fancy terms for things in order to sound more upper class. While the actual upper class didn't use any of these words because they knew they were upper class and the whole point of being upper class is not caring a damn what anyone else thinks.
U / non-U is not a 'proper English' vs. lower-class thing
Solution 3:
For the most part, I don't think there is such a speech divide in the USA.
Britain is much more noted for the association of class and speech than is the USA, where speech patterns are more likely to indicate region of origin than social class. In the USA, social class is more likely to be linked to income (money, economic class) than anything else.
(In many parts of continental Europe, regional differences account more for difference in language use than does social class.)
If there is a U / Non-U divide in the USA, then it is more likely rooted in economic status than anything else. You generally won't find impoverished "aristocrats" (ex-moneyed people) in the USA who maintain a sense of exclusivity based on diction or vocabulary used. There, that would be absurd. In Britain, perhaps not.
One may want to reflect on what basis a certain sociolect might presume to claim the title of "upper class". Seems to me more a sense of entitlement than anything else.
In the USA, an interesting distinction could be the difference between what one does and what one has done (in the sense of a causative). I think that would be a marker of social class in that society.
Solution 4:
No, it doesn't exist in America at all. There is no minority dialect for the privileged which the majority buys into. No one who speaks the standard dialect thinks "we're not good enough to talk that way." No one says "you are trying to get above yourself." There are certainly cases of minorities (racial and otherwise) that discourage members from leaning the standard dialect, but there is definitely not a privileged dialect that the majority accepts as superior. Rich people who affected a very formal, old-fashioned dialect would be laughed at.
The closest we might come to it is with technical language. If you aren't really a scientist or a scholar, you aren't entitled to use that sort of language. But it has nothing to do with class.