As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.
In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:
A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.
The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.
There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.
On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.
Background
First, I don't find the statement "If a parenthetic expression is preceded by a conjunction, place the first comma before the conjunction, not after" in my 1979 edition of Strunk and White (Macmillan, 1979), but I do see it in the on-line version (May 1995).
Second, in the 1979 edition under the rule "Enclose parenthetic expressions between commas", the authors state:
"This rule is difficult to apply; it is frequently hard to decide
whether a single word, such as however, or a brief phrase is or is
not parenthetic."
So, I'm not sure it's correct to attribute the statement "If a parenthetic expression is preceded by a conjunction, place the first comma before the conjunction, not after" to Strunk and White; after all, they were long gone by 1995. Also, Strunk and White acknowledge explictly in the 1979 edition that the rule is difficult to apply, which means to me that at times some judgment may be required.
Your Question
In your question, you state:
I disagree with the comma placement in the following example: "He saw
us coming, and unaware that we had learned of his treachery, greeted
us with a smile."
To me, it makes more sense to place the comma after "and", not before
it. That is, to write: "He saw us coming and, unaware that we had
learned of his treachery, greeted us with a smile."
I wouldn't go so far as to say your usage is wrong, because I don't think it is -- I understand the logic and sense of it -- but I prefer Strunk and White's placement. To me, the sentence sounds better when I read it out loud, at least the way I read it out loud. How it sounds is what matters. I'm not sure the following is grammatically correct, but I sometimes use two commas:
He saw us coming, and, unaware that we had learned of his treachery,
greeted us with a smile.
For me, this sometimes lines up well with the pauses in the sentence, and it is not inconsistent, or at least not entirely inconsistent, with the 1979 edition of Strunk and White. In any event, we now have all three possibilities out on the table: comma before the "and", comma after the "and", comma before and after the "and".
Best Answer
I believe there is a comma after "read it" in the third example in Strunk and White's Elements of Style. I'm looking for a version of the book that does not include the serial comma in that example but haven't found one.
Revision: I found one. It was a PDF copy of an older edition so I couldn't see the publication date. It appears that there was a typo in some versions where the serial comma was left out. Later prints include the serial comma per the style guide's recommendation.
Sorry, another revision. I forgot to give a link to a current copy: http://www.feedbooks.com/book/3697/the-elements-of-style