heres a hint
TEC-straightforward power units, relatively cheap with a good eco to back them up. other than that however, they are really nothing special. more or less they are the beginner race, just about pumping out units and taking down your enemy.
in a head to head battle of pure horsepower, the TEC win hands down
Vasari-although their ships are tougher than the TEC's, they are also disproportionately more expensive. without the eco base that the TEC have a head to head fight will probably end in failure for the vasari. however, the vasari have especially powerful capital ships, relatively strong upgrades and the ability to zip around the galaxy using their phasegates (in addition their "mobility" techs are lower than any other races, making them ideal early expanders to other systems/through wormholes) the key with the vasari is picking your fights so that you dont lose your precious, expensive units. a well fortified phasegate network will help you do that.
Advent-havent played much with them, but from what I've seen I'll give it a guess.
because they are "unity" based, the advent have a bunch of REALLY weak ships, they start out relatively weak but as you progress, spread your culture throughout the universe, get increased group-buffs from your caps and get defensive structures down (correct me if I'm wrong, theres one to increase AM right?) the hoard of small units becomes a hoard of powerful swarms, individual buffs on the cheap ships (2?!?! 2 is how much they cost in terms of fleet points!??! are you Fing kidding me!?!?!) can turn a losing battle into a clear and decisive victory
I'll get back to the advent more as I play as them.