I don't want to offend anyone, so if you find this topic distasteful, skip this one.
A friend from the South told me an anecdote about a "rooster". Just back from the U.K., I note that Brits don't hesitate to call the male bird by its original name.
My thoughts turn to euphemisms (in both countries) for the place where my British contemporaries used to go to "spend a penny"--that's the coin they used to need, to obtain access to a "public convenience". In Britain, the upper and middle classes go to the "loo". I noticed that some Brits (notably on the BA planes which took us to and from Heathrow) have adopted the Canadian term "washroom", which I had not heard across the Atlantic until this last trip. That's really a variant on "lavatory", the normal term when I was growing up: it wasn't a place where you went to wash. I heard "bog" used in England, also.
At my British "prep school" (aged 8 through 13), matron was always ready to hand out a laxative to those who answered in the negative to "Have you been through?"
In the U.S., I tend to prefer "john" to describe the "s***house", where a stepdaughter once expanded my vocabulary by saying she was going to "dump a load".
In the British Navy, I learned to use the term widely known by yachtsmen and others on vessels of all types, the "head". I've read of the place being called the "Jakes", but not met that term in conversation. "Toilet" is widely used by English speakers. "Would you like to wash your hands?" really means "Do you want to use the loo?".
Another expression from the UK, widely used, is "W.C." this stands for "water closet", and probably dates from the 19th century, when this invention superseded the outhouse. The famous plumbing specialist of the early 19th century, Thomas Crapper, has given his name to the water closet, although he didn't actually invent it. He might be dismayed by knowing how the first four letters of his name have come to be used.