In order, from left-to-right, of the classes on the class select screen:
Scout: He's probably around the same age of his voice actor: Nathan Vetterlein (so 30-ish).
Soldier: I believe he wanted to fight in WW2 but was rejected by every branch of the U.S. military, and the game takes place in the sixties. Assuming the Soldier was just old enough or a little older (let's say 20) to enter the military during the war, that would make the soldier about 40.
Pyro: You got me.
Demoman: Judging by how elderly the demo's mother looks in the official comics, I'd say he's in his 40s.
Heavy: The Heavy got new voice lines in one of the updates (I think the "Tale of Two Cities" one) about how he's getting too old for fighting so I would say he's no longer in optimal body shape...which means he's probably around the same age as demo.
Engineer: I haven't come across supplemental material that might put his age around anywhere so I'm going to take a guess and say he's around 30. He apparently has eleven PhDs but I'm not sure how long it would take to achieve a feat like that.
Medic: He has a medical license (okay...he had a medical license) so he must have spent quite some time at medical school. I don't know how long he's been a mercenary so I'm just going to be cliche and say he's around 40.
Sniper: I'm going with 40. Not much for me to go with. He spent years in the Australian outback perfecting his skills as a sniper and his voice also suggests a not-so-young age.
Spy: Unfortunately his mask obscures any wrinkles he might have so it's hard to come up with some reasonable range. Let's say he's 40 and that most of the mercenaries met at their high school reunion.
