Just finished my first 4p medium map with them.. 6 hours and 14 minutes lol
I absolutely love them. Tough i didnt use the phase stabilizers a whole lot..
What i had to realize tough was that the Vasari are huge techjunkies. If you dont research, you wont make it past the 2 hour mark, at all.

I started off with just colonizing about 3 other planets (2 of them asteroids ), researching my pop cap on both the ice worlds and the terran home planet, developing them as best i could.
A few imperial research centers for the pop cap tech, and i built TWO media hubs in my home planet fairly quickly, just an impulse decition really.
Then i discovered the tech that gives Vasari units 20% (or something) damage bonus in their own culture-space.. Wow.
With my culture spreading at 5 per sec i was getting a nice damage bonus everywhere i needed to be. And the AI's were forced to do the same, they also built 2 media hubs on one of their each fringe planets, which i had never seen the AI do before.
Awesome to see how they actually react to your tactics.

Anyway, then later on, as i said i hardly used the phase stabilizers at all, i just went for the old sledgehammer approach, which i did NOT think would work with the weak Vasari ships (but hugely expensive and sucking up fleet-cap).
But it did! With as much military research as possible, i completely ravaged their forces, never lost a single capital ship.


Some tips for using the Vasari as sledgehammers:

Research: Focus on the first line of damage tech for whatever ship you like the most (skirmishers or the missile frigates).
After thats taken care of, go for as much armor as you can, then for the health/regen tech.
And finally, as much shield tech as you can afford. I spent ALOT of my early hard earned credits on those 3 lines of research, very early.. It was hard to afford any ships at all to defend my planets, but in the end it meant i could focus on pumping out ships for every single credit, with awesome shield and armor protection!
And DONT forget about the life-sustaining antimatter-tech, without the extra antimatter storage/regeneration, the hearts of your fleet (your support cruisers) wont work very well

Combat: This is the second most important thing about the Vasari..
Since you cant face the enemy head on in a fair fight, you have to use what unfair tech the Vasari has availible to them. Such as the overseer cruiser which boosts & repairs your ships health points, and the Something cruiser that first of all can weaken the shields of enemies and allow phase missiles a greater chance to pass trough it.
And with some research it can phase-warp TO, and completely disable ships around them (yes, area of effect!) for ONE MINUTE.

Say that you have 50 missile frigs, and 5 such cruisers with 3 overseers..
You will end up with a force that first automatically disables any ship GROUP it encounters, for a whole MINUTE, while it also weakens the shields of them enabling your missiles to pass trough the shields completely occationally.. This means that if you have done your research, you should have about 40% or so chance to pass trough the shields.
Thats 20 missiles out of 50. That will completely ignore the shields. Against capital ships or shield-heavy ships this is devastating to say the least.
All while the 3 overseers automatically heals and boosts the health of whatever ships are closest to death, with 30hp/s healed, a single frigate can tank an entire Kol battleship..

In the late-game to mop up the planets i'd recommend getting as many of the devastator capital ships as you can, since they are the only real vasari ship with great health and weapons (what? ) that also has insane planetary bombing skills, such as placeable siege guns and at lvl 3 you can get them up to 100 planetary bombing damage..
When the enemy is weakened, you can just swooch 2 of those in to make the kill, defence structures and the planet itself.

I love them )