Brilliant recollections there XM!
The Woodhouse ground was before my time but my father in law, who was a prominent local footballer used to mention this ground in his football tales he'd regale me with.
I certainly remember United playing at Dore (maybe Brunsmeers ground these days?).
When I had my (failed) brief flirtation trying to break into the pro game with United, they fielded 5 teams most Saturdays.
1st team, reserves in Central League, Juniors in Northern Intermediate, usually Saturday morning on Ball Inn, 4th team in Hatchard League and a 5th XI in the S&H Under 18 league, playing at Concord Park. The U18's were managed (in the loosest sense) by a bloke named Lol Swallow, whose main function was to get 11 players together as being the bottom of the pile, the teams above nicked players at last minute, ruthlessly!
The NIL team was generally full time apprentices and the odd 1st year Pro and occasional amateur.
The Hatchard League (a tough, first rung senior football league covering South Yorkshire) was made up of amateurs, triallists and the odd apprentice Pro, a real steep learning curve for young aspiring footballers.
The under 18's also used amateurs and triallists and was the start point for many wannabee pro's.
Football in the 50's,60's & 70's was phenomenal in its participation figures.
Every ability was catered for in the endless leagues that existed back then...
But that's another debate to be had maybe another day...