As for the difference between "jetzt" and "nun": that's really tough. There might be a subtle difference, but we are talking about nuances most German native speakers arn't able to put their finger on. "im Augenblick" on the other hand is different. "Nun" and "jetzt" are often used to describe a present state that was influenced by a process in the past or a process in the present that is likely to influence the future. "im Augenblick" is not used to emphasize such a sequence!
Examples:
1"Wir haben eben gegessen, nun/jetzt sind wir satt"
2"Nun/jetzt bin ich satt" ~ even this implies that you've just eaten and thus arn't hungry anymore.
Substituting "nun/jetzt" for "im Augenblick" in 1.) isn't correct and subtituting those words in 2.) would alter the meaning to ->3.
3"Im Augenblick bin ich satt" ~this on the other hand simply means "right now I'm not hungry" or "for the time being I'm not hungry"
Another thing that is noteworthy is that there are alot of German idioms containing "nun" and "jetzt" where the words can not be used interchangeably! Examples: "nun denn", "nun ja", "jetzt gleich", and so on.
Maybe someone studying German academically can point out the more subtle differences or historical differences that used to exist between "nun" and "jetzt". That being said right now I cannot think of an example where changing jetzt to nun or vice versa would raise any eyebrows in a real world scenario. If anything "nun" is becoming a bit obsolecent in favor of "jetzt".