Right, cards on the table. While I have seen Star Wars, I have never read Lord of the Flies or Lord of the Rings and I’ve never seen Michael Flatley dance.
First of all is determining the location of the fight. Let’s assume it takes place on planet Earth at some undisclosed location. Flatley and Ralph would remain the same as they do in real life. Sauron also would remain more or less the same since his power isn’t specifically tied to Middle-Earth, but rather comes from his own skill. (He specifically pours some of his power into the One Ring, so we’ll assume the Sauron that’s fighting is the one that existed before the creation of the One Ring). Darth Vader, however, is a tad screwed.
All Vader’s power comes from the Force and Obi-wan (in Episode 4) says that the Force “is what gives a Jedi his power. It’s an energy field created by all living things. It surrounds us, penetrates us, and binds the galaxy together.” 
He specifically says it binds the galaxy, not the universe. Thus we can infer that the Force is specific to the Star Wars galaxy. Each Star Wars film also makes it clear that Star Wars happened ”A long time ago in a Galaxy far, far away.” 
Hence Vader has no ability to use the Force in this galaxy or during any fight taking place in this galaxy.
Second of all is the use of weapons. In order to be fair this should be a bare bones knuckle fight, so no lightsaber, no Ring of Power, no swords, etc.
Now 3, 2, 1…FIGHT
Ralph would be out of the fight rather quickly. As shown in Lord of the Flies, Ralph is not a violent person and has a tendency to be polite and logical even in the worst moments. Towards the end of the book he chooses to run away and hide rather than fight and possibly be killed. It’s reasonable to assume that Ralph would not stand much of a chance and would be killed or seriously injured within a few seconds. So that’s Ralph out of the way with Vader, Sauron and Flatley left.
Many of you may not be aware that Vader’s Suit has quite a few mechanical problems (as demonstrated in James Luceno’s book Star Wars – Dark Lord: The Rise of Darth Vader). The fact is that without the Force or his lightsaber, Vader is a weak disabled man in a badly made suit. Michael Flatley however, is a trained amateur boxer (seriously!!). I believe that several hard punches from Flatley (or Sauron) into the various machine parts on the front of Vader’s suit and it would be far too damaged to continue.
So it’s the Lord of the Dance vs The Lord of the Ring!
This is a bit more difficult to see who would win. Just to make it easier I will list each of their positive attributes.
1) Isn’t encumbered with a heavy metallic suit of armour.
2) Proficient flute player.
3) Trained amateur boxer.
4) Holds Guinness World Record for a tapping speed of 35 taps per second (and thus is incredibly fast) 
The Dark Lord Sauron:
1) Is approx 8ft 11 inches tall.
2) Has the ability to shape shift (In The Silmarillion alone he transforms into a great wolf, a serpent and a vampire)
3) Has an incredible ability for deception 
On the face of it it looks like Flatley would get his ass kicked by Sauron. However, I think this might not necessarily be the case.¹
Firstly being tall is not going to scare Flatley. He’s perfomed in front of literally millions of people and someone towering over him is hardly going to scare him.
Secondly I don’t think Flatley would fall for any of Sauron’s deception. After all he’s been divorced once, falsely accused of rape, been screwed over with creative control on Riverdance and didn’t even bat an eyelid when he was diagnosed with facial skin cancer. 
The only issue is whether Flatley could tap, box or flute play into defeating a wolf/serpent/vampire. But even then I don’t think it would get that far.
If you read Morgoth’s Ring (the tenth book in The History of Middle-Earth Saga), there are several points made by Tolkien in describing the motives of Sauron, of which one is “it had been his virtue (and therefore also the cause of his fall …) that he loved order and coordination, and disliked all confusion and wasteful friction.” 
Sauron loves order and coordination. Now imagine Sauron sitting in the front row of this performance.
Seriously, could you get any more coordinated? Sauron would have loved this! Flatley’s performance would have utterly convinced Sauron that Flatley is an equally big fan of order and coordination. Thus I don’t think Sauron would have fought him and by definition Flatley would have won.
So in conclusion… Michael Flatley is the true Lord of the Universe!