This is a an exclamation of extreme discontent that is meant to go beyond a simple "god damn it," or "fuck that." You can only say this phrase three or four times a year, or else it loses all meaning. It is Special. When you stub your toe in the middle of the night, it is a "god damn it" situation. When your car breaks down hundreds of miles from friend or family, at 3:00 AM, in the rain, and you just filled the gas tank, that is a "motherfucker" situation. When you decide to walk to work because it is such a nice day, only to hear a strange, whistling, noise, then look up and see a large A-bomb headed your way...that is a "shitburgers and dick cheese!" moment.
Huang just had morning sex with his wife in Hiroshima in 1945, and felt like a jolly good stroll. While petting a puppy and eating cotton candy, he looked up and saw a strange object hurtling towards him. He realized those crazy fliers about a giant bomb might be true and thought to himself "shitburgers and dick cheese," at least I got laid.