I'm curious if there was a single sword fighting technique that all knights used, and how much it varied from person to person.

Yes and No. There were common, widely used systems but it would vary from region to region depending on local flavours of armour, weapon choice, etc. Period is by far the most important factor though.

Did knights have their own 'style' within that technique?

As much as any martial artist has their own style and technique, yes.

Were there any knights that used an especially unique or unorthodox style and what lead to this?

You could argue that people like the masters listed below had their own unique styles and their success lead to a wider use of that style. For example, Fiore Dei Liberi was a soldier before he was an instructor. Perhaps someone with a deeper knowledge of the medieval period will be able to provide some anecdotes :)

Were there multiple overarching techniques or 'schools of sword fighting'?

Oh yes :)

Bear in mind that arms and armour have evolved substantially over time and techniques vary over both time and region to account for that. A Viking fighting in mail with a short sword and shield is going to be using very different techniques to a plate-armoured medieval knight fighting with a longsword, who is going to be employing very different techniques to a Napoleonic era officer fighting with pistol and Sabre. Similarly, someone fighting on a ship may be more inclined to wear lighter armour and use a short sword, whereas a cavalryman might want heavier armour and a longer sword more aimed at thrusting than cutting. When you look at it in this context, it makes sense that there were regional styles and techniques.

Loosely speaking before about 1400 we don't have much to go on - we can look at weapons and make educated guesses about how they were used, but can't say definitively. But after that period we start to have existing, printed manuals published by masters of the day, with illustrations, describing techniques and so on.

Probably the most popular works from the 15th century are Hans Talhoffer's Fechtbuch and Fiore Dei Liberi's Flos Duellatorum in Armis. Both are widely in use today and you'll find many schools around Europe and the US teaching these systems. If I had to pick out any archetypal "Medieval Knight" style, it would probably be Talhoffer.

Moving into the 16th Century we have Albrecht Duerer's Fechtbuch and George Silver's Paradoxes of Defence. Note that although all these manuals deal with various weapons, by Silva we're really starting to see a trend towards almost exclusively educating civilians in the use of civilian swords. You wouldn't roam around town with a Zweihander - although it could certainly help in a fight - but you could conceivably carry around an arming sword. By the 1600's we're thoroughly into rapier territory, with manuals like Hale's The Private Schoole of Defence and Swetnam's Schoole of the Noble and Worthy Science of Defence (gotta one-up that title!). By the 1800's or so we've evolved again into Sabre territory - not that other swords weren't used, just that Sabre's were the primary sidearm of the day - probably the most popular of which is Hutton's Cold Steel.

If you're interested in further reading:

http://wiktenauer.com/ is a fantastic resource that has all the sources listed above and then some

http://wiktenauer.com/wiki/Masters - a list of the masters with link to biographic pages, treatises and more

/r/hema /r/wma - Historical European Martial Arts on Reddit

https://www.youtube.com/user/scholagladiatoria A youtube channel run by Matt Easton, a HEMA instructor and seriously good swordsman

https://www.youtube.com/user/SkallagrimNilsson An entertaining Scandinavian living in Canada with an enthusiasm for all things involving metal

https://www.youtube.com/user/lindybeige Historian / Archeologist / Reconstructor / Dancer / D&D Enthusiast / Whatever else seems to pop into his head

Edit: Thinking of unorthordox techniques, remember that the most important thing in a duel is to end him rightly!

Edit edit: Updated sources