Since you don't seem to care about all of the alien races I am just going to answer for the ones you mentioned in your question.
Sources are multiple discussions on forums, my own experience, and various wikis.
The Mass Effect universe isn't very clear about how old Krogan can get.
Almost all of them die while doing what they're good at (Mercenary work, fighting).
Okeer is probably the oldest Krogan you meet in the game. He has fought in the Krogan rebellion, which happened a long time before the events in Mass Effect. It is even said Wrex has fought there, meaning Wrex would be around 1000 years old. Wrex calls Okeer old, which means that Wrex with 1000 years old probably isn't considered old for Krogan standards. A fair age to guess for Okeer would be around 1800 years old. Even though Wrex called him old, it's not clear if he actually is nearing the end of his lifespan.
It's pretty safe to assume Krogan can live for thousands of years if they don't die by unnatural causes. They really are tough.
Turians and Quarians
Both the Turians and Quarians aren't very special compared to humans. Especially the Quarians aren't that different from humans (As mentioned by Tali).
While also here it doesn't seem like there is a confirmed max age, it's safe to assume they will live for around 150 years, just like humans. Quarians don't always reach this age though, because they are very vulnerable to infections. It's why they wear the suit after all.
Just something I came across during my search. Apperantly Vorcha only live up to 20 years.