Actually, Americans wouldn't say "fourth July" – that would likely connote "the fourth iteration of July" in some longer timespan (e.g. "In the fourth July of my adolescence").
"Fourth _of_ July" (or "July fourth") are the Americanisms here.
"Fourth _of_ July" (or "July fourth") are the Americanisms here.
Actually pronouncing it carefully with a clear "of" emphasizes the date, either for clarity or because it's otherwise important.