It's an expression which almost certainly means "I'll be damned (to hell) if I do". At a certain time (1940s), swearing was forbidden in American movies. So the script writers created replacement phrases [damned > danged]. Adults understood the real meaning, but children didn't. I can't imagine anyone actually saying this expression. Other expressions such as "I'll be danged," "dang it," "dang you" were actually used in the 40s and 50s by religious people who wanted to swear but didn't want to use bad words.