I think this is going to be challenging. I think you may have to focus on Game as the "thing" you want to look at.

(This is going to be mostly obvious, but bear with me.) If you think about a game, it's between two teams, Home Team and Away Team. So one way to express that is
Team--(1,M)--Game instead of just one join between the two tables, you have two, like this:

HomeTeam (alias for Team)---(1,M)--Game--(M,1)--AwayTeam (another alias for Team)

So one way to think about it is:
1. a table of teams with team information
2. a table of games, with joins to the Team table, so the Game table would have something like
GAME(HomeTeamID, AwayTeamID, HomePoints, AwayPoints, Date, Location...)
Then you'd have Team(TeamID, Division, TeamName...)

Okay, what about Excel?
If you put all the Excel files for this in the same folder, you can use a Folder source in Excel and then combine all the sheets... Then when that's done, you can import that into Access (well, the Teams and Games tables that you basically create using PowerQuery).

I guess you could do this with linked Excel tables, but I think it would be a pain. up to you though.