The Three Races are gargoyles, humans, and Oberon's Children, the three known sentient species native to Earth. Gargoyles were the first to appear, followed by humans. The Children of Oberon incubated in magic and "evolved" third, hence another name for Oberon's Children is "the Third Race." 
Gargoyles and humans both came into existence in the same way, but Gargoyles makes no statement as to whether this was by evolution, creation, or both. 
New Olympians are a hybrid race, and fall somewhere between mortals (generally humans, but also other, non-sentient species and perhaps gargoyles as well) and Oberon's Children, rather than as a separate race of their own.  Vampires and weres exist, but are not proper races; rather, they are mortals with a supernatural condition. 
The term "Three Races" encompasses only the sentient races native to Earth. Other sentients exist elsewhere in the universe, including the N'Kai, Space-Spawn, and a third (as yet) unnamed alien race that make up the three major powers in the Milky Way Galaxy.