They are functioning as direct objects. I don't think that makes them nouns.
I agree, they are nouns: "where" means "a place" and "when "a time" here.That is a very odd analysis.
For me, the sentence says "Who said what, (who said) where, and (who said) "when"? These three "w" words are direct objects of "said". The comma after "where" indicates a list.