How do I determine my wheel size
I too own a Trek 520 and the bike does indeed come with 700C wheels and has for quite a number of years. 

The labeling of a 700C tire is somewhat misleading due to historical reasons. 

Originally, tires were sold in sizes based on the outer diameter of the tire. 700A, 700B, and 700C tires were all 700mm in diameter. However, the 700C tires were the thickest and the 700A tires were the thinnest. This difference was made up by using a smaller diameter rim for 700C tires and a larger diameter rim for 700A tires.

Nowadays, all tires labeled as 700C mount on a 622mm rim. Most tires will have both labels on them. 622 is the size recognized by the International Organization for Standardization, or ISO but 700C has become so common that it is the de facto industry standard label and is how most people will refer to that size. 

Tire widths are (sort of) an additional complication. This page has a chart showing what widths tires are compatible with what width rims. However, I have run all sorts of widths on my 520, have never worried about rim compatibility, and have never had a problem in that respect. (I have mounted one brand of 700x35 that was big enough to rub on my frame, even though lots of others worked fine.)

All of this information and more is available on Sheldon Brown's tire sizing systems page, which is a fascinating read if you want to dork out over tire sizes for a while. 

The following is in response to your edit:

It is not correct that you can mount a 26" or 27" tire on your 622mm rim. 26" and 27" tires are two different entities and each mounts on a different size rim. A 26" tire mounts on a 599mm rim and a 27" tire mounts on a 630mm rim.

Also be wary of 28" tires. While some mount on a 622mm rim, others mount on a 635mm rim.

When in doubt, trust the ISO number and stick within the widths on the chart mentioned above.