comma - only one element of style

I agree with you on all counts.  Only I don't like  the  sandwich ',and,'  at all.  It looks forced, and seems to draw undue attention to itself.

It can also work like this: Since you are ok with 'He saw us coming, and greeted us with a smile' ( and I am too) , what if one sees the 2nd comma (in the original statement) as not related to the 1st, but just as a way to break up the long sentence?

And there is also the matter of how the music sounds when read aloud, or even played privately in your  mind.  This is quite a different kind of utility of the punctuations.

"He saw us coming, and greeted us with a smile."  Why is there a comma in that sentence?  Maybe there is a rule I am unaware of, but I would write it without a comma.  With that, I agree with Robert about the sandwiched and, and I agree with Anna that "unaware that we had learned of his treachery" should be set apart.  Your quote from Strunk and White is not logical and it makes me wonder if it might be a typo.

Anna said

If I wrote the same thing, I would have put the comma after "and"
What would you say?

The same. I know this is heresy, but Elements of Style is overrated as a writing guide. If you want a larger and far superior book to improve your writing, I recommend The Sense of Structure: Writing from the Reader's Perspective.

I agree with many of the sentiments expressed. Without any regard to authority or reason, if I were to punctuate the original sentence, I would omit the comma before the and and add one after the and.

He saw us coming and, unaware that we had learned of his treachery, greeted us with a smile.