The thing I like best about you is your well-formed question and honesty, the thing I like second best is your awesome quote from Knute Rockne!
To your question: I think you should start with personalities, and strategy, then deal with tactics, (cat, dog, etc.)
Bob Diaco is the defensive coordinator and no one is neutral about him; Cinci fans hated him, ND fans loved him at first, hated him after Navy and loved him again after he showed up at 4:30 AM to land uber-recruit Ishaq Williams. (see threads)
The first thing about a 3-4 is it is an odd front defense. (five men across the line of scrimmage.)
Next is Diaco's philosophy; bend don't break and disguise coverage, oh, and also play as many players as you can. That is so the players in the game can be counted on to perform at the highest level possible.
Over the past several seasons, at Cinci and ND, the offense has been quick strike, not on the field for long periods as with a ball control offense. Those are the most important strategic points; if you want more, then you are a bit of a masochist. What recent ND fan isn't?
As far as Cat and Dog, you are referring to the outside two of the four linebackers. One has pass rush and run coverage predominantly, the other falls off into coverage for passes to the flat, short passes, the running back out of the backfield, etc.