TEC strengths: economy and they have good frigates (especially LRM). All their ships generally have more armor and hit points than those of other races. Their capital ships especially are difficult to destroy.

TEC weaknesses: capital ship special abilities are significantly inferior (with a few exceptions), crappy strikecraft (especially bombers), and late game their support cruisers are significantly inferior to those of other races.

Advent strenghts: culture, Illuminator vessels, stupidly powerful capital ship special abilities, best heavy cruiser in the game in terms of firepower vs cost. Their support cruisers are also fairly potent, especially the Guardian. Subjugator isn't as impressive as the Guardian, but still quite useful.

Advent weaknesses: crappy economy, Illuminators are expensive so getting them in numbers fast is somewhat problematic, very susceptible to being rushed on small maps, light frigate is basically useful only as a distraction or to make (almost certainly suicidal) attacks against support cruisers with its steal anti-matter ability.

Vasari strengths: powerful ships, decent economy, can capture neutral extractors more easily than other races, can usually defeat numerically superior fleets, phase missiles, probably the best strikecraft (although Advent is very, very close). Good capital ship abilities (not as good as Advent), and awesome support cruisers (Subverter and Overseer).

Vasari weaknesses: ships tend to be costly both in terms of resources and supply points. Light frigate is too costly to be truly useful.