NOTE: These are our guesses unless marked otherwise. Only Barnaby and Kaede have officially confirmed ages within the series.
Kotetsu: 34-36
We know his age is closest to Sky High’s VA Go Inoue’s, who is 33. Barnaby’s VA Masakazu Morita comments that he’s not that far off Kotetsu’s age himself (he’s 39), so I doubt Kotetsu would be younger than Inoue.
Barnaby: 24-25
Barnaby is confirmed 24 on 1st cour, 25 on 2nd. His birth date is NC 1953/10/31.
Antonio: 33-35
Antonio’s slightly younger than Kotetsu.
Keith: 27-29
We could be really off with this, but Keith seems older than Barnaby judging from his appearance. Definitely not over 30, though. (Insert mental images of 30 year-old virgin.)
Nathan: 30ish (?)
Nathan’s definitely not younger than Barnaby, but not as old as Kotetsu. We’re having really hard time guessing her age.
Ivan: 18-19
Seems to be confirmed to 18 on 1st cour, 19 on 2nd in some early production notes, which haven’t been included in the official books.
Karina: 16-17
Confirmed 16 on 1st cour, 17 on 2nd. The production notes with her age haven’t been included in any of the official books.
Pao-Lin: 13-14
Confirmed 13 on 1st cour, 14 on 2nd. The production notes with her age haven’t been included in any of the official books.
Yuri: 30-32
Yuri looks about 14-16 in episode 16. We don’t know how far in the past that flashback is, but it’s not further than 15 years.
Kaede: 9-10
The second character whose age we know for sure. She’s confirmed 9 years old on 1st cour, 10 on 2nd.
This is Sternbild 
I think Ivan is older than Barnaby, since Barnaby refers Ivan as his senior from the Hero Academy (IIRC). Not because Ivan has became a hero longer than him.
He refers to Ivan according to their current status as heroes, and Ivan’s been a hero longer. They didn’t go to the academy at the same time, but Barnaby was aware of the incident with Edward.
The students of the academy are in quite a big age range (like that sweating lady who looked way older than the rest), so they normal graduating times probably don’t apply to Hero Academy.