All characters have been aged up by around 4 years:
Aang - 16 or 116 years (115 + 3 months to be exact), born 16 BG
Zuko - 20 years, born 79 AG
Yue - 20 years, born 79 AG
Sokka - 19 years, born 80 AG
Azula - 18 years, born 81 AG
Katara - 18 years, born 81 AG
Toph - 16 years, born 83 AG
Since Aang's thawing out of iceberg, the story happen within 9 months time period, being thawed out somewhere in December and war ending in September.
No, it's not strange that Aang will start his training in other elements so late. Yangchen, the previous avatar who was an Airbender, started her training in other elements at 21.