Strangelove and Thank You... were great. Many of Charlie Chaplin's films were clever and hilarious satire of his generation's woes ( totalitarianism, industrialization, poverty, etc.). Gold Rush, Modern Times and The Great Dictator stand out. Duck Soup was a funny slapstick and absurd movie that mocks militarism and totalitarianism. It featured the Marx Brothers.
Although I'm not a fan of his later films,a lot of Woody Allen's films have a satirical bend to them. Shadows and Fog (film noir/1930s Europe)), Zelig (history) and Sleeper(future, futuristic scifi) were all smart and funny, reminicsent of his great stand-up schtick.