I'd say all of these in Britain. Perhaps the first is most commonly heard, but I'd say they're all OK. The only other option would be "on July sixth" (without the article) which is most commonly heard in the States.When's your birthday?
1. It's on the sixth of July.
2. It's on July the sixth.
3. It's the sixth of July.
¿Qué primaría en un contexto británico?
Las dos primeras cambian el orden y la última elimina la preposició 'on'.