attack antimatter and research your phase missiles, and shield/hull upgrades. the Kortul's destructive nanites and overload (I think that's what it's called) abilities are pwnage when combined with phase missile swarm from the Vulkorus.
Space egg is awesomeness with nano-disassembler and gravity warhead. get one/two.
other than that, lots of Skarovas, Kanraks, and flak frigates (Advent are strikecraft heavy).
the Skarovas will keep the otehr ships away, Kanraks do lots of damage with phase+AoE missiles, and flak kills any fighters.
keep about 10-15 Stilakus Subverters and 5-10 Overseers for repairs behind the front lines
but that's my opinion on general Vasari tactics. fell free to deviate partially or entirely from this to counter their specific fleet.