According to the intro movie, an experimental mobile weapon's lab activated something (looked like a phase gate) 10,000 years ago. So the Vasari have been running for almost ten centuries.
It's probably that this race is either a civilization that exists within phase space, or exits on the other side of the galaxy, or universe. It seems like to me, that since the Vasari have had no contact with the enemy other than to drive them insane, that they aren't your typical race.
Even the Vasari communicated with their subjugated races, and they did experience the occaisional rebellion. Safe to say, that no matter how much two factions hate each other, they do communicate.
So, in my opinion, the unknown race the Vasari are fleeing from are either a machine-type race, either the result of some creative race or a race themselves that integrated themself, or a hive-type race, like the zerg or ants (but they use real ships, no organic ships, please!).
On a parting note, you should take game values with a grain of salt when applying them to backstory. Ironclad HAD to balance the game--they couldn't make it so the Vasari could roll over everyone at 1:3 odds, or that the Advent are easily able to kick TEC's keister's all along the front.
Really, the only reason the TEC has been able to resist the Vasari is became one they're so freakin' rich and they're so freakin' big. They have almost unlimited manpower and probably massive infrastructure in place for resources and ship construction. The Vasari are, essentially, limited to the, at most, few hundred million of them that escaped. This figure may have increased or decreased, drastically in some cases, depending on how they breed and what sacrifices they had to made on their journey. However, each ship that they lose to the TEC is a ship they can't readily replace, especially the crew.