Welsh speakers may like to be reassured that hwyl is included here because of its unEnglish look, not because it’s thought intrinsically odd. It is, of course, a Welsh word, but one that has become widely enough known in British English to be included in most dictionaries, though users often mispronounce it.
This is how it was described in Garthowen, by Allen Raine (1900):
Will was certainly an eloquent preacher, if not a born orator, and possessed that peculiar gift known in Wales as “hwyl” — a sudden ecstatic inspiration, which carries the speaker away on its wings, supplying him with burning words of eloquence, which in his calmer and normal state he could never have chosen for himself.
That’s much how it’s understood in English. But in Welsh the word more often refers to a complex and intangible quality of passion and sense of belonging that isn’t easy to translate but which has been said to sum up Welshness in a word. The Geiriadur Prifysgol Cymru (the big dictionary of Welsh recently published by the University of Wales) lays out its ramifications like this:
A healthy physical or mental condition, good form, one’s right senses, wits; tune (of a musical instrument); temper, mood, frame of mind; nature, disposition; degree of success achieved in the execution of a particular task &c; fervour (esp religious), ecstasy, unction, gusto, zest; characteristic musical intonation or sing-song cadence formerly much in vogue in the perorations of the Welsh pulpit.
Its origins lie in a much older sense of the sail of a ship and hence elliptically one’s course — in life rather than on the sea. Most broadly, in Welsh hwyl refers to a person’s mood. By itself it can also mean “goodbye” as a common short form of hwyl fawr, roughly “all the best”, as can pob hwyl.