What’s the pre-invasion galactic population?

Trillions. Councilor says so in Mass Effect 1 I believe, which should mean 3 trillion or more inhabitants, if not a far greater number since no one says trillions for 1 or 2 trillion people. We are talking about 2000-3000 years of space travel history, depending on race, colonization and technological and medical progress, all while said space travel is near instantaneous thanks to Mass Relays. Even so the galaxy is greatly under-populated since I'd expect the population to be more in line with quintrillion to decillion inhabitants.

Let's say that a typical developed country's capital city has a population of about 5% of the country's total population (https://en.wikipedia.org/wiki/List_of_national_capitals_by_population). The ratio of homeworld population to total population of long-spacefaring races should be about the same (because both should be Pareto distributed) so if the turians' or the asari's homeworlds populate in about 6 billion each, the whole races' population can be estimated to some 120 billions each. Repeating the Pareto distributions reasoning to total race populations, I'd say 1–3 trillions is a realistic number.