On page 212 in the book, it is mentioned that the distance from the southern coast of Black Marsh to Lilmoth is approximately 15 miles.
Cross-referencing this bit of information with the map of Stros M'Kai from Redguard (which has a latitude/longitude grid), as seen here:
http://www.imperial-library.info/sites/default/files/gallery_files/redguard_map.jpg
... as well as this map made from the Arena map, which shows the island of Stros M'kai below Hammerfell (one island though, so I estimated distance by pixels to help calculate).
http://www.imperial-library.info/sites/default/files/gallery_files/cyrodiillargelowrescr7.jpg
using the above map, I measured in pixels the distance from the center of Lilmoth to the southern coast of Black Marsh, which was appox. 47 pixels.
ignoring the scale on the bottom of the map, which is clearly wrong based on what the novel tells, I then measured the number of pixels that fit between the two east-west lines on the first map, approx. 3/4 the pixels, so i rounded down to about 10 miles per 0.25 degrees.
Assuming Nirn is spherical (duh), the circumference of Nirn should be approx. 14,400 miles. About 58% the circumference of Earth.
This makes Nirn's total volume about 5x10^10 miles cubed. Compared to earth's 1.09x10^12, this is about 4.5% the volume of Earth, at least according to my math.
Wow, Nirn is tiny.