Fighting the Vasari...

You dont fight the Vasari. You submit.

The only thing I can think besides simply outnumbering and outproducing them is to kill the subverters first, you will have a much easier time with them dead.

I have actually found it easiest to engage Vasari fleets when I either have superior numbers or the economic muscle to replace lost ships at a very high rate.  Oh ya and also an Akkan with Armistice.  So I jump in and get into a protracted battle.  Both of us are slugging it out.  If I start to lose I just activate armistice and jump out with my fleet largely in one piece still together.  While all this is going on I have the fleet replacement getting constructed as they get destroyed.  Then bring replacements up to the frontline.  Lather. Rinse. Repeat.  Seems to work just fine.

The overseers are who are probably hurting you the worst.  They have an ability that increases armor, but in the way that Sins uses armor the effect is the same as increasing health.  So if you are focusing on a carrier with a bunch of overseers around, you are doomed.  Instead of focusing all your fire power on the carrier focus on the overseers or assailants.  The carrier cap ship has an area of effect heal that can be defeated by luring their ships away by moving away what ever it is they are attacking of yours. I usually send my fighters to take out assailants lurking in the back and use the shooter frigs and caps to focus on an overseer or more often focus on the veritable cloud of skirmishers. From my observations, the caps dont seem to do as much damage and are much harder to kill than the swarms of little frigs.

If you've got a Dunov hanging around with EMP Bomb, use it on the largest cluster of Overseers/Subverters you can find. It'll deplete antimatter and shields from all ships within its area of effect.

As always with TEC, their primary strength is the survivability of their ships once Hoshikos enter the picture, as well as armor upgrades (up to +6 armor for every single ship).

On top of what HolyLime said, as TEC, you should be able to produce replacement ships more easily than a Vasari opponent in terms of build time (especially if you have Industrial Juggernaut researched) and cost. The point where this advantage is mitigated is when the Vasari player gets RA up and running and/or when Enforced Labour (credit cost of ships -8%) and Optimized Construction (resource cost of ships -8%) are researched.

If his one opponent has RA, then he SHOULD submit. At least, pre-1.1.

But yeah, I'd say your strategy is having a replacement fleet in the works while fighting. But kill those Subverters; between screwing up your armor and disabling your ships, you want them dead. Their Assailants also have massive range and area-of-effect added to their attacks, so kill them. Those two ships combined are the Vasari's trump card; Phase Missles and the ability to lower your resistance to Phase Missles. Vasari ships are top-notch, so pound for pound, they will break you. Your, hopefully, superior economy is your saving grace. If you are on a small map though, you might have trouble.

You're invited to come test out some of these strategies in online multiplayer once you feel comfortable with the game.  It's the "Ironclad Online" button.

Yes, stop playing the silly AI and join us on ICO!