I don't think there's any difference in meaning, although "free of charges" is much less common than "free of charge". Regarding your second question about context: given that English normally likes to adopt the shortest phrasing possible, the longer form "free of charge" can be used as a means of drawing attention to the lack of demand for ...
The fact that it was well-established long before OP's 1930s movies is attested by this sentence in the Transactions of the Annual Meeting from the South Carolina Bar Association, 1886 And to-day, “free white and twenty-one,” that slang phrase, is no longer broad enough to include the voters in this country.