Recently, i ran into a fleet of mostly carriers (20 or so), a level 8 Kortul, and level 10 Skirantra, and a few other ships.
If we're talking about capital ships level 5+, then it's very likely that we're over an hour into the game. With a normal difficulty AI, possibly as far as two hours. Basically, by this point, anything goes. I've heard of people achieving over 600 credits per second income within two hours. The bottom line is that if the enemy fleet is considerably larger than your's, the answer probably lies 30-60 minutes in the past (or even longer) when they built up a superior economy to support it.
What are some of the nasty tactics that people use when playing as Vasari against the AI (in general, and specifically against the above mentioned scenario) to overcome a larger AI force?
Hangers with phasic traps. Don't build any strike craft, and save all your antimatter for this one ability. This will completely shut down huge quantities of their strike craft and render them easy prey to your units. As Vasari you don't have a great unit for chasing carriers (in theory it's the Skirmisher, but it kinda sucks) but against the AI you should have no problem making due with Assailants.
Make sure to bulk up on phase missile research, this can really boost your damage a lot.
Also, I am not that impressed by the damage output of a starbase. The one weapons upgrade tooltip said it was good against structures. Is it also good against ships as well?
Starbases deal fine damage; I don't know what your issue is here. The first attack upgrade for the Orkulus is actually not as bad as it first sounds. It may deal less damage than the other weapons, but it attacks fewer targets meaning this damage doesn't get spread out over the enemy fleet (which can make it easier to absorb). The best damage-upgrade for the Orkulus is its second, however. Phase missiles are absolutely awesome weapons once upgraded, and their base damage is rock solid to begin with.
If a static defense doesn't have much damage output (for the cost), then it really doesn't seem to help in saving one from upgrading to the next fleet supply and just getting more ships to defend.
Use repair platforms to boost your defensive longevity. Static defenses can be a downright pain to take down with a good formation. They're no substitute for fleet, but against the inflexible AI they will easily handle any direct assault it might throw at you.