It sounds like something Ned Flanders would say.
I believe it just means "nothing at all". But what are the origins of the phrase? Is it common in the US as well as the UK?
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The following is what I've found on the net about this phrase:
The Random House Historical Dictionary of American Slang lists the original form as "Doodly-squat," dating from 1934. No clue given as to the origin. Doodle means, variously, a fool, a Union soldier, a penis, to cheat, and to copulate. The dic does not list a usage for "doodly-shit" until 1966.
The dic lists "diddly-squat" as a euphemism for "diddly-shit," which does not appear until 1964 (1963 for diddly-squat).
It is difficult to draw a conclusion from all this, except I doubt it has anything to do with squatting in a dwelling.
Dave Wilton, posting in alt.usage.english
I have also found an interesting story about the etymology of the phrase.
(Editorial note: The copied story has been removed because of questionable copyright use. Also, the linked story is a joke and not a true etymology of the phrase.)