Metric vs imperial

I hear "July fourth" as much as I hear "fourth of July". What's curious is that I hear both of those more than Independence Day which is the actual name.

Huh, I never heard july fourth, but then again I don't live in america and I've also only heard fourth of july a handful of times

"The Fourth of July" is longer and sounds more formal than "July Fourth." "The" is a definitive and often a marker of formal English, it implies it is not just a date, but holds significance. English also doesn't like to have two stressed syllables in a row, so the "of" breaks it up. It's more about "branding" that date. In common parlance Americans use either format, or "Independence Day" as suits them. Until the late 19th century the British wrote dates mm/dd/yyyy which is where America got it from. Other European countries with influence on England (like France) used dd/mm/yyyy and the English picked it up. The US kept the "old" way because of far less geographic neighbors to need to standardize with, and a general aversion to being compared to the British. The US military uses dd/mm as a multinational force that works with NATO, it avoids confusion in coordinating efforts, but still uses mm/dd in civilian correspondence.