SPOILER
Well, Strangelove isn't playing with a full deck of cards, which is why he has those outbursts. Plus he can't control his right hand, which is why he does the salute. In fact, the real life illness was named after the character I believe. The final scene just showed the madness of all the politicians, Strangelove's stupid plan, the Russian taking photos for his country. The "I can walk" part was probably a really random outburst. I can't really explain it, but it was just an unexpected, funny moment.
SPOILER END

IMO, this is the best satire ever, and Kubrick's best from what I've seen, closely followed by A Clockwork Orange.