JFK Assassination responsible for this films Oscar wins
Let me explain.
JFK was assassinated on November, 1963.
Doctor Strangelove was due for a wide release in December of 1963. However events in Dallas caused studio to push release back for several weeks.
As a result the film was not elegible for the 1963 Oscars - and left Tom Jones to claim the main prizes in a field of very ordinary films.
http://www.imdb.com/mymovies/list?l=32397724