All of these are common in NZ ("twaddle" is a bit old-fashioned). I had no idea "nonsense" was supposedly regional, and four dictionaries I just checked make no mention of that (and include American sources of quotes).
twaddle is word I haven't heard for a long time (I moved from the UK to Australia 27 years ago). It's a great word!
It is a lovely word, indeed, and it is undeservedly heavily underutilised, hands down.
I find myself using it nowadays rather sparingly and mostly in just one phrase (and its semantic derivatives): «all that twaddle […]».
Rubbish, nonsense, drivel, and claptrap all recognizable to me, a Yankee. Twaddle is a new one tho!
I would say nonsense was quite common in the US. Otherwise agree (although I would get the meaning).
It is all pants to me (I was actually «translating» pants into Universal English).