Inverted Clauses

He kissed Jade.
That's standard word order for an English clause. The subject comes first (unless preceded by an introductory phrase). Most word orders simply don't work:
Kiss did he Jade
You knew that.

But there is an inverted word order that does work.
Jade he did kiss.
That makes sense. The object has been moved to the front of the sentence. (And “did” was added.)

Grammatical status? I've never seen it called ungrammatical, even in discussions of this construct. I also have never seen it mentioned in a grammar book, and for that I'm guessing oversight. So call it marginally grammatical. As you probably guessed, some authors use it, but no one uses it often, which is consistent with a marginal status.

Some authors must use this construct just for variety, but I have already stated my negative opinion about variety just for the sake of variety. Giving that this is an unusual construct, it is going to be more difficult to read. So an author should have good reason for using it – even though there is a more familiar way of saying almost exactly the same thing.

This is my favorite use of object-first, from Anne of Green Gables (Montgomery):
"You don't want me!" she cried. "You don't want me because I'm not a boy! I might have expected it. Nobody ever did want me. I might have known it was all too beautiful to last. I might have known nobody really did want me. Oh, what shall I do? I'm going to burst into tears!"
Burst into tears she did.
Oddly enough, Given/New does a reasonable job of explaining this. That idea says a sentence normally starts with the given information, and inverting the phrase accomplishes that. Think about possible rewrites:
1. She burst into tears.
2. She did burst into tears.
3. She did burst into tears.
The new information in that sentence is, in a way, did. #1 leaves that word out and in a way contains no new words. So #2 is probably the better rewrite, even though it's an extra word and IMO it's not easy to show emphasis with helping verbs.

That leaves #3, which I think nicely puts an emphasis on did. The problem is, at least to me, the italics makes her crying seem unexpected. That doesn't fit the story and isn't what the author wanted. That particular use of inverted phrase is so distinctive I can notice when authors don't use it! #2 inverts the phrase
1. ...all the while her voice encouraged him to rest, to sleep. And he did. (The White Dragon, McCaffrey, page 232 paperback)
2. ...all the while her voice encouraged him to rest, to sleep. And sleep he did.
And he did is a perfectly grammatical sentence, but to be meaningful it has to pick up a word/idea (sleep) from the previous sentence The problem is, while it's easy to pick up the front of a sentence, picking up the end is difficult (Simple Phrase Grammar: The Hidden Grammar of English).

So it's an awkward sentence. That problem can be easily fixed with
1. And he did. [original]
2. And he slept.
3. And he did sleep.
4. And sleep he did. [rewrite]
This is the same issue as before – the real information is in did which is missing in #2. The author, given a choice between did and slept, chose did. #3 contains did and adds the needed information. But #4, inverted, puts did in a position where it gets more emphasis.

I don't think an author can be criticized for not using an unfamiliar construction (though I am not fond of the excuse of not knowing about it). Ironically, the author used that construction in dialogue:
"Saving people they were." (page 391)
He pointed to the worn boots on his feet. "New they were." (page 289)

Some other examples where the Given/New explanation works well:
“Want a drink?” asked Hollenbach. “A drink I don't need, Mr. President, not after Scotch and five wines tonight.”
(Night of Camp David, Knebel, page 10 trade)

It would place him in the role of a candidate, he said, and a candidate he was not. (Night of Camp David, Knebel, page 153 trade)
Another elegant usage:
Kim had many amazing qualities, but subtle she was not. (Juska, If We Had Known, page 34.
Subtle could be called Given, but that's a stretch. We can, however, guess that the author wanted an emphasis on not. Here, the alternative works just fine:
but she was not subtle.
I would not have read that and thought that phrase should be inverted. Yet I think the inverted phrase is better. Reasons unknown.

To me, it's usually an object that gets moved. Or, when a verb is moved, it becomes a participle.
1. She fell into the water, and I thought she didn't know how to swim, but swimming she was. 2. She fell into the water, and I thought she didn't know how to swim, but she was swimming.
It is very common to say swimming is part of the verb in #2, though in fact it could be a participle. Inverting the phrase I think makes it a participle (if it wasn't already).

This inversion is of just a prepositional phrase.
1 He kissed me on the lips
2. On the lips he kissed me.
I don't know how to categorize the following, except it is my second favorite inversion. After being caught in a very awkward situation:
“Please excuse us. Paula's had some awful news. Her mother died.” ...I saw the client's face trying to readjust itself, wobbling toward sympathy, but finally settling on puzzlement. Grief did not a bra on the coffee table explain. (The Opposite of Everyone, Jackson, page 63)
Does it have other uses? It slows the reader down, so one use is to slow the reader down. The above can be explained neatly in terms of Given/New, but it might also slow the reader down to appreciate a very awkward moment for the character.

An inversion could clarify the target of a modifier. #1 is ambiguous -- the modifier at the end could modify workers or the firing. #2 and #3 clear up the ambiguity with an object first construction.
1. I fire the workers with a lack of enthusiasm.
2. The workers I fire with a lack of enthusiasm.
3. The workers with a lack of enthusiasm I fire.
Um, no one worries too much about that and I don't think I've ever seen a phrase inverted for that reason. A simpler solution:
With a lack of enthusiasm, I fire the workers.
I fire the workers who lack enthusiasm.
By the way, several of these constructions strung together can sound like poetry:
Hurdles I jump,
Obstacles I avoid,
Goals I seek,
Frustration I find.
And, inversion combined with left-dislocation creates Yoda in Star Wars:
To answer power with power, the Jedi way this is not.
So it's a way of creating the mood of a fantasy language while still making things clear.