“Pew” is by far the older; the OED has it from 1603. “Phew” is from the same year, oddly. And “Pooh” is a few years older (1593, probably derived from “poop”).
P.U. was a cute spelling for “pew/phew” – you can see how it might have arisen, especially since one spelling variant is “pyoo.” If you say the word slowly, it sounds like “P.U.” It was certainly extant by the 1940s – Warner Brothers cartoons used it, meaning it was probably more acceptable that others.
“P.U.” (spoken) is an exaggerated way of saying “pew,” which is a slangy way of saying “phew.” I have never seen it written “pyoo,” only “pew” or “P.U.”
So while your friends would be justified in mocking you heartlessly for writing “pyoo,” they’re ignorant clods if they don’t recognize the pronunciation (pyoo = pew).
Here in Indiana, the folks at Indiana University (I.U.) in Bloomington seldom miss an opportunity to giggle at a P.U.-stink joke about Purdue University (P.U.) in West Lafayette. :rolleyes: