I would imagine the School Managers was exactly what it sounds like - a group of School Governors
The Order of Oddfellow (Manchester Unity) was a subgroup of the Oddfellows Friendly Society. I haven't found anything about your g-grandfather's particular branch but there are others mentioned on the National Archives website.
A sick and Dividing Society was very often based in a pub - in your case "The Woolpack". Members would "pop in" each week to pay their subscriptions and probably have a pint or two as well. If any members were too sick to work during the membership year (usually Christmas to Christmas) then the kitty would pay them an agreed amount in lieu of wages. This wouldn't be a fortune but would at least help out a bit. At Christmas, if there were any funds left over, they would be shared out among the membership (hence the Dividing in the title).