For people who haven't seen the movie, it's all about the sex.
For those who have, it's all about religion, or cults, or what in the heck were they doing at that orgy?
What most people who have commented on this film seem to have forgotten is that EWS is based on a novel by Austrian author Arthur Schnizler, and had been a pet project for Mr. Kubrick since about 1960. This accounts for some of the anachronisms in the film: in Austria in the Twenties, when the book was written, it would have been a rather ordinary thing to go to a private ball or a masquerade, everyone knew a good deal about Beethoven, including at least the plot of Fidelio and secret societies, especially among the upper classes, were a much-discussed, but seldom-seen, part of life in Vienna. (The Hapsburg Empire had a secret police that was the lineal ancestor of Stasi, Mossad, the KGB, and the SS -- quick, efficient, direct and sometimes not too heedful of the niceties, hence, people who had odd political ideas, or other quirks, tended to keep things under wraps.) OK, so it's got something to do with the Bavarian Illuminati...your point? In Vienna, it would be like saying it had to do with the Elks, the Jaycees, or the Odd Fellows -- they had much larger fish to fry. He wanted it to be set in 1960's New York, but as time went by, he found it harder and harder to sell it as a 'period' film, thus the somewhat pieced-together version we have now.
Of course for a family like the Harfords (who were originally a middle-class Jewish family, not unlike that of Schnizler's pal Sigmund Freud) a ball such as Ziegler's would have been a once-in-a-blue-moon treat, and the more lurid portions would have been part of a world they perhaps saw, but preferred to pretend they hadn't. Yet, it's interesting to note how much of what seems "modern" in the film, would have been even more apropos in the era between the wars.
Cocaine and heroin were cheaply and plentifully available from pharmacists and less respectable sources well into the twenties, especially in Europe. Also in the Twenties, the evangelical/Pentacostal/Fundamentalist strain of Christianity was considered a bizarre, regressive fringe...progressive, forward-thinking people were vegetarian nudists who read Nietzsche and the Bhagavad-Gita. Cult religion, from nature worship to the O.T.O., was about as unremarkable as it is now -- Christianity was intellectually on the ropes, and had even less authority back then than it does today, and it's to be noted that at one point, the Bauhaus design school (in neighboring Germany) seriously contemplated instituting long red
robes (like academic gowns, but closed) with pendant necklaces and cropped hair as a school uniform. (However, to clarify, Mr. L. Frank Baum was a Theosophist -- a Westernized form of Buddhism -- not The Golden Dawn, certainly not "several occult groups" and he would have been somewhat shocked to think that anyone would think of him as a Satanist, or exponent of sex magic.)
But what were they doing?
Short answer: Kubrick made the ritual up himself, out of whole cloth, after asking Jocelyn Pook for some "weirdo" music (his words). She handed him a tape she'd made of a Roumanian priest chanting an Orthodox prayer that she'd backmasked and accompanied by her violin playing, she'd titled "Backward Priests". Cleaned up and made a bit longer, it's called "Masked Ball". Twenties-period erotica was heavily into fantasies involving masks, blindfolded servants, and people dressed in ecclesiastical clothing, often in luxurious settings -- all Kubrick did was to take these and ramp them up a bit.
Longer answer: In the original, the woman who "redeems" Dr. Harford is dressed as a nun, and there was a strong religious component in the story. He's Jewish, and is dragged before a man who resembles God the Father. His wife's dream, which is sketched in broad terms in the movie, in the book runs to some pages and was supposed to have closely followed the events of Harford's night of horror -- a woman begs to run away with him, a group of students (read cadets, who liked cutting up each other with sabres) gay-bash him, he visits a prostitute, he gets caught up in a bizarre party attended by monks and nuns -- and gets crucified, while all the while, she's popping corn (so to speak) with a variety of strange men.
I repeat, this type of scenario was quite common in historic erotica, and was especially favored by high-end bordellos in Catholic countries, and in French Revolutionary secret groups. I've been told that the novel was "third rate" (I beg to differ), but if there ever was a sexual component to the Illuminati, it would have been closer to the book -- without the human sacrifice, of course!
Unlike the movie, the book ends with him trying to decide whether to tell his wife. Since few backers could stomach the idea of a crucified Cruise, he was forced into dragging out the action into a long weekend, and the orgy got turned into the Carnival in Venice/ritual heirogamy that you see on screen.
Just for kicks, here's the text of the prayer:
"And God told to his acolytes...I give you a command...to pray to the Lord for the mercy, life, peace, health, salvation... and the forgiveness of the sins of God's children. The ones that pray, they have mercy and they take good care of this holy place."