When you say "no possible direct object", do you mean direct quotations...

No, quotations are not objects of any kind. In all of this discussion, if a verb of speech is being used, it is entirely irrelevant whether there is a quotation or not.

...or no direct object, as in qajatlh...

Yes, that's what I mean. In fact, it's "no explicit object: either not possible or obviously not meant." It's possible for jatlh to have a direct object, but when you say qajatlh, you obviously don't mean I speak you as a language.

... or do you mean, like in *qajatlh*, that *you* cannot be the direct object, because a person cannot *be spoken*, and thus it must be the indirect object?

That's part of it, yes.

The reason why *qajatlh* is an instance of the "prefix trick" and not an instance of a verb taking an object with the semantic role of the indirect object, is just that we were told that the object of *jatlh* is a language, an act of speech or the thing that is being said, but not an audience,

Yes.

 whereas we know that *ja'* can also take an audience as object, right?

Yes.

However, in the thread I was referring to you can also find the sentence *tlhIngan vIjatlh* ("I speak to the Klingon").

I don't see that in the thread you linked to. I see tlhIngan Hol vIjatlh, not tlhIngan vIjatlh.

 Would that be an instance of the "prefix trick"?

No, that would probably be considered an error. Someone probably forgot to add Hol to indicate that they were speaking "Klingon language."

Are there other verbs apart from *ja'* (and maybe *jang*) that can take an object with the semantic role of the indirect object?

Probably lots of them. ghojmoH is an example. In paq'batlh we see both [puqloDwI'] vIghojHa'moH and QIt ghaHvaD yIn Hegh je vIghojmoH. In the former, the student is the object; in the latter life and death is the object in the role of direct object, and he is the beneficiary in the role of indirect object.

(And if that elided object in the first one concerns you, try ghojwI'pu' chu' ghojmoH jatlhwI'pu' po'qu' from qepHom'a' 2013.)

"But that's got -moH!" I hear you cry. So what? The only thing -moH does is give the subject (syntactic role) the semantic role of causer instead of agent or theme or whatever. All the stuff people have said over the years about objects becoming subjects and so on is just more tortured grammar rules.

-- 
SuStel
http://trimboli.name