could you please do me a favor? Gimme some concrete examples to explain the nuance between "all" and "all of" to help me better understand it?
thanks in advance.
There's no nuances of difference in meaning of the words themselves, Jeff, but several minor differences in grammatical usage. It's a bit messy, but here's a summary of Swan, Practical English Usage:

1) Both OK before nouns with a determiner: 'All (of) the cake is gone; all (of) my friends are gone.' It is the determiner that makes the noun specific, not the 'all (of)'.

2) Only 'all' if no determiner: 'All people like pie; all sugar is sweet'.

3) Only 'all of' before object pronoun: 'All of them are hungry; all of it is gone'.

4) Only 'all' after object pronoun: 'She ate them all; he made it all himself'.

5) Only 'all of' with complements: 'Are those all of them?; that is not all of the pie'.

This is not a complete picture, but should cover most of your concerns. Perhaps other members can cite more guidelines.
That's covered by Mr. M's (Swan's) first rule. my is a determiner. Both are correct. Make an arbitrary choice.

(By the way, those aren't sentences; they're phrases.)

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Whoa, thanks very very much, Mr. Micawber.
Now I got a pretty clear picture of that. haha. See, I've already bookmarked this page for reviewing in future.
What about the sentence "all of my talented students"? Is that correct, or should I say "all my talented students" and why? Thanks!!
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 CalifJim's reply was promoted to an answer.