I defer to John McKinnon on the origin of "diddly-squat." However, I will add that it is quite common to hear the similar form "you don't know s- -t." In any case, the expression is what it is, and it means what it means.
"Double negatives" are interesting. Expressions like "I don't got none," "It ain't goin' nowhere," and "I ain't gonna do that no more" are said to be bad grammar, which they are. The correct forms are "I haven't got any," "It isn't going anywhere," and "I'm not going to do that any more."
It is sometimes said that the reason double negatives are bad is that "a double negative becomes a positive." That's not really true. In informal speech, a double negative simply intensifies the negation. "I ain't got none" does not ever mean "I have some."
Oddly enough, in educated speech there is an example of a double negative meaning a positive. This is the "not un-" construction. George Orwell criticized it in "Politics and the English Language." "A not unjustifiable assumption" means a reasonably justifiable assumption. "Not unlike a seventeenth-century Shelley" means rather like Shelley. He suggested "curing oneself" of the "not un-" habit by "by memorizing this sentence: 'A not unblack dog was chasing a not unsmall rabbit across a not ungreen field.'"