Did Strasberg get the nomination because he ran the acting school and it was good politics to nominate him?
Absolutely. Politics is all over the Oscars. Strasberg was old, GFII was his first co-starring role in a major movie, and he had mentored countless big stars, including Pacino and Brando. Time to give him the Oscar.
That said, Strasberg actually turned in a worthy performance in II. Consider that the Academy rewarded Liz Taylor for recovering from a near-death experience by giving her the Oscar for "Butterfield 8," one of her least-distinguished roles; and Sidney Poitier at the height of the civil rights movement for "Lillies of the Field," when he'd done far better work in other films.