The Squire is the leader of the side and the decision-maker; deciding what is danced where, when, how and by who. It is also his responsibility to lead and teach the dances.
The Bagman (literally the Man who keeps the Bag) is the team secretary, responsible for communications within the side, taking booking requests/invitations from outside parties & sides, and monitoring who is attending which event.
Old Man (2016)
The Old Man is essentially the Chairman of the side; chairing meetings and settling disputes that may occur within the side on the rare occasions that they arise.
The Treasurer, as you would expect, holds the purse strings, taking receipt of payments and processing the accounts.