beemind.me has Trello integrations for “root mean power of card ages” and “sum of card ages to some power”. It doesn’t have “oldest task in Trello” though.
As for “oldest Gmail message”, I searched the forum a bit and found @adamwolf mentioned he has a script for this, but hasn’t published it. If there’s enough interest, I could try making this as well, but considering Beeminder already has an official integration for the number of Gmail messages, I wonder if that could easily be extended to do oldest message/message age as well.