What does Silver Tongue work on?

I'm sorry, I never used it. But what I have read about it, is that it is a skill like the beastlord "tame" than can be used on trained units, this is, units that AI has trained in a city. It is not valid for beasts, monsters, champions, summons, etc. Only trained units. No need to say a Garrotte is not a trained unit...

Is it worthy? I think not, as I don't see AI deploying powerfull units, but some people find it interesting...

Maybe if you find a yithril juggernaut, you could try to "tongue" it (but again, not on an scaped juggernaut, I guess that is not considered a "trained unit").

Interestingly, you can also use it on Syndicate Thugs, which means you can get some 'cannon fodder' units that don't ask for any wages (may be a bug).

Trained units would be soldiers for the most part.  I use it all the time to take a unit of mages, archers, horsemen, from the enemy AI during combat.  It doesn't work on Jugs, as far as I know.  "Trained' usually refers to things that a city can produce, but I know it doesn't work on Jugs, and I doubt it works on henchmen or Golems.  Kind of funny that "Diplomat" gives you an ability that only works when you are at war, not peace.

But, I had no idea it worked on Syndicate, that's interesting...

Yeah, didn't know it worked on Syndicate, never seemed to work on Bandits, so I'm not sure what the distinction is there.

Generally, it's just basic units as Xia says, not fancy ones like Juggs and Golems. During Beta it worked on "wild" Knights of Asok and that became my favourite trick for a while, but they seem to be a lot less common these days, have only encountered one Asok camp since release and wasn't playing as a Diplomat at the time.

It's most useful once the AI starts fielding tougher units, don't waste the influence in early wars. I had some fun stealing Clan of the Crow from Tarth and that sort of thing. I imagine there are other strategic uses for it, like subverting enemy pioneers to your cause (since the AI often includes a pioneer in its stacks) to prevent the AI from settling or to steal a prime city location. An expensive way to do it, but in certain situations could be handy.

Does it work on garrison militia/archers? Never tried, but have wondered ...

And if it does not work on Juggernauts, is it fair to assume it wont work on Ceresa's city-trained spiders, either?

That's make no sence as well, spider can't be reason and bride to...I guess it's only work on common solder who can be bride, but not a monster who don't care about a gold or men but repect to one who training them this way...unless you beastmaster..

Yep, but you don't get to have them stick around afterwards they just... spontaneously bite it after the fight.  Which you can sort of understand.  They're not supposed to be around except for city defence.