Some observations:
1) Oral vs. literate
"No one" occurs 1.6 times as frequent as "nobody" in FLOB while in BNCdemo "nobody" is 2.5 times as frequent as "no one".
The frequencies of "none" in written and spoken English are very similar, with 80 instances in FLOB and 72 instances per million words in BNCdemo.
A similar pattern in the whole BNC:
"No one" occurs 108.93 times per million words in the written section and 60.92 times in the spoken section; in contrast, there are 143.98 instances of nobody per million words in the spoken section and only 49.84 instances in the written section.
The distribution of none in the written and spoken sections of the BNC is more balanced (94.47 vs. 72.43 instances per million words respectively).
2) Usage
None is typically followed by of indicating a scope*, which accounts for 62.5% of the total occurrences in FLOB and 47.5% in BNCdemo.
[We choose to make a distinction between this scope usage of "of" and its usage indicating property (e.g. no one of my age, no one of that name)]
The contrast for the written and spoken sections of the whole BNC is not as marked (54% vs. 51%), which shows that none is followed by of over half of the time in both written and spoken English.
In contrast, nobody is never followed by of indicating a scope while no one rarely occurs in this structure. No examples of the two types were found in FLOB and BNCdemo, but there are a total of 17 instances of no one of in the whole BNC, all of which occur in the written section. A more commonly used substitute is not one of (e.g. Not one of these is really um professional, BNC: KCV).
3) In relation to nobody and no one, none is also felt to be more emphatic - my intuitions.