Does a double negative in ancient Greek mean an affirmation, i.e. ‘everyone’, or just an emphasis, i.e. ‘no-one at all’?
No, actually not 
Double negatives in Greek emphasize the negative.
A concise explanation of the repetition of the negative from one of my favorite books: A Parallel of Greek and Latin Syntax: For Use in Schools, p. 169
A new post quotes ἡμεῖς γε οὐδὲ ἐπινοοῦμεν τοιοῦτον οὐδέν from Xenophon, where οὐδὲ … οὐδέν amounts to a single negative. “We for our part are not even (οὐδὲ) contemplating anything (οὐδέν) of the sort.”
Cf. English “I didn’t say nothing” meaning “I didn’t say anything.” That’s substandard usage in English, but perfectly standard in Greek.
However, if the longer negative comes first, each negative operates independently. So οὐδέν οὐ (lit “nothing not”) is tantamount fo “everything.” (That’s the same in Latin and other languages, incl. English.)