The best way to use vengeance is if the enemy is focusing all their units against a single starbase or capital ship.  There's really not much to be said here; the more units are attacking the target, the more damage will be dealt.

Keep in mind the advertised amount isn't quite as good as it may seem.  The damage reflected by vengeance effectively goes through armor and mitigation twice, so it's greatly reduced.  Maxed out you're advertised a 200% damage returned rate.  This goes through mitigation and armor, then gets reflected, then goes through mitigation and armor again.  You'll probably only end up getting a 30% damage returned rate at best, and this damage is diffused over a large number of units (highly suboptimal).  Personally, I think vengeance is highly overrated and a much weaker ability than most people make it out to be.  It's not terrible, but nothing special.

Now, vertigo is a real game-winner in the right time and place.  Vertigo at level 3 will cut the damage of affected in units in half.  It has a large area of effect and an unlimited target cap, and a fairly decent duration.  Stack it with other forms of damage reduction and you have a scary defensive combo!

The "Holy Trinity" can be used to refer to both the Progenitor(malice)/Rapture(Vengeance)/Radiance(Animosity/CB) combo as well as the Progenitor(shield restore)/Rapture(vertigo)/Halcyon(EAA/TKP) combo, depending on who you talk to.  The former went out of favour when malice was nerfed eons ago and it hasn't really been worth the expenditure of three capital ship slots since.  It works, but not nearly as well as advertised.  Back when malice was uncapped this could propagate into a lot of damage, but now that it's capped it's actually quite weak given all the setup needed.  For most reasonably-sized fleets, the second combo works far better by simply stacking a bunch of offensive and defensive abilities.

Yeah, ever since Malice got killed, Vengeance has had a lot of its usability cut down...  If it was something more like 150%/300%/450%, then it would actually do well in the current system.  I still say the malice nerf (the way it was done) is my least favorite nerf in the history of the game, but eh...  Nothing I can do about it aside from mod it back for my own personal use.

Anyways, vengeance is still best used with Malice, though that doesn't do that much anymore...

Yes. It also works if you use the Rapture's ultimate ability to take control of an enemy's support cruiser. The only thing is they won't have their researchable abilities obviously, but luckily those two both have healing abilities by default.

If im playing multiplayer and the map is big, plus im on a good spot on the map thats jumps away then i think it is possible. 

What about 1 rapture (vertigo,  Aura), guardians , 2-3 carriers. Hoshikos or overseers will support the cap and envelop other units. Depends on allies. Strong?

Really think advent caps should always level up themselves from the start. Everything depends on caps for their strength. 

It won't be big enough.  Good players can reach you within 30 minutes even on the most ludicrously massive maps, and they'll have spent the time building an economic infrastructure so they can shove a massive amount of units down your throat.  While this will still give you more prep time, you won't be able to get a mature force on the field.

You'll get swarmed and annihilated by someone who just masses basic combat units here.  Heck, if I spied something like this I'd smack you with a T0 disciple swarm; 60-80 disciples isn't unheard of by the time you could have all those units on the field.  Needless to say, that's game over right there.  You need more firepower.  Remember, for the mere price of researching guardians I can build an additional 7-8 combat frigates.  Combat frigates need to make up the backbone of your fleet, and then you add more advanced units to the mix.

First of all, you should always lead with either Progenitor or Halcyon.  The Progenitor offers you the ability to rapidly colonize and build an economy, which on larger non-rush scenarios is simply too good an offer to pass up.  The Halcyon is by a longshot Advent's strongest combat capital ship, and on smaller rush-scenarios is virtually necessary for survival in the more competitive multiplayer scene.  Rapture should always be second capital ship at earliest.

Second of all, always make sure to get firepower first.  The trick is to phase in the more advanced support units over time.  These units are expensive to research and have little firepower addition to your fleet, so the enemy will be hitting a lot harder with more combat units.  This means you need a sufficiently large force of combat units before you can introduce these support units.  TEC can bring out hoshikos earlier because their repair power is especially effective for smaller fleets, whereas Guardians scale nicely and are more effective for large fleets, so you'll need to hold off on them.  Also, if you don't yet have a Progenitor, it's usually only worthwhile to build guardians for the repulsion ability.  Their shields just deplete too quickly when using shield projection without shield regeneration.

Thirdly, carrier cruisers are a poor choice for an early unit.  Because of their slow move speed, they have a very difficult time retreating, and their antimatter can become depleted quite easily from repeated phase jumping and strike craft replacement.  This makes them very poor unit choices.  If you want carriers early-game, you should build multiple Halcyon carriers.  They have no antimatter costs for building their strike craft, they move considerably faster, and once they reach level 3 (maxing out Adept Drone Anima) the number of strike craft they field is close enough to be competitive with carrier cruisers anyways.

Advent have problems with TEC and Vasari in the early game, ever since the Illuminator got a bug for it fixed, hopefully the latest main beam weapon buff has made things better, I can't exactly find out due to technical difficulties.