Verdict:

From the posters and that famous bomb cowboy scene, this film appeared to be just an absurdist dark comedy, but I think is pretty awesome is that it is also a terrific action and drama movie. The scenes of the fighting between troops looked like camera footage from an actual war. The events inside the warplanes are also shot seriously and the actors play it straight. In fact, most characters are playing it straight, with just a bit of over-acting for comedic effect, and there is a real sense of tension in what happens. This relatively serious approach makes the humour all the more striking.
Dr. Strangelove is not really a comedy in the standard meaning. There are no punchlines. The humour comes from the situational silliness and the way the dialogue is delivered. Any jokes are subtle, there to remind you that this is satire, like the fact that characters are given silly names or when the tune of “The ants go marching” starts playing with Major Kong wearing his cowboy hat. There is a constant contrast between the seriousness of the situation and the simplistic animalistic human behaviour.
Since Kubrick is at the helm, you know that all the dialogue makes sense, and everybody’s performance is top notch. Peter Sellers plays 3 different people, all with very distinct portrayals, delivering comedy gold. The way he nonchalantly fiddles with the belt of the machine gun is already so adorably hilarious.
The primary theme is the critique of Cold War-era nuclear arms race, in which the means of obliterating the human race are in the hands of imperfect humans, any of whom could exhibit mental instability or just stupid behaviour. Given how difficult Kubrick was in real life, it is amazing that he created a comedy that is this funny, with a subject that was probably the most not-funny subject at the time, or since.
Dr. Strangelove is a timeless and unique dark comedy, and its underlying messages are still relevant as they are more about human behaviour in general than about the nuclear weapons specifically.