The actual meaning of "nazi" is not equal to a member of "Hitler's party", nor does it necessarily refer to "Hitler's party" at all, as it is simply a shortened form of "Nationalsozialist", i.e. national socialist, or (more generally) the ideology of "Nationalsozialismus", national socialism. Even today there clearly are people holding - more or less - such kind of views, so one might call those nazis without them (perhaps) being related to any specific political party. In fact, that's what is done in (at least) Germany today, even if, sometimes, the prefix "Neo" (Latin for 'new') is added, in order to differentiate a contemporary nazi (by calling him/her: Neonazi) from the nazis of actual Nazi-Germany.
I have heard of the usage of "uber" (meaning something like "super"). I didn't know it might be considered objectionable.
I don't think it is considered objectionable, unless one feels compelled to consider quite anything of German origin objectionable. As far as I know, the way into the English language of uber-/über- is similar to that of another German prefix: eigen- (means "self-", or "own"), like in eigenvalue, eigenfunction, etc. While these evidently are scientific terms, it seems possible to me that uber-/über- has a similar origin in English, as it may stem from another quasi-scientific, more exactly philosophical, term: Übermensch (mainly associated with Nietzsche). I'd guess that at least many philosophical trained speakers of English (only) are able to make something of "Übermensch", so this could be an explanation of how uber-/über- arrived in English.
Come in handy, these cute German prefixes, don't they? ;-) (After all, uber/über maybe sounds not so strong as super-, or hyper-, so it permits a higher grade of nuance.)
(Edit: By the way, most basically, über- in German means exactly the same as over- in English: overburden = überbürden, that's it. Over- and Über- also have the same etymological roots and in this sense über-'s "re-arrival" in English really seems a bit ironic. You've got, essentially, the same word twice.)