Species doesn't work because, clearly, humans, elves, and orcs are all the same species.
Exactly.
The standard dictionary definition not-withstanding, in science some different species can interbreed and make hybrids - some of them with apparently just fine fertility. Humans & Neanderthals, or different types of Macaws seem to do just fine out to at least three generations so far. And there's the Beefalo. With a bit less robustness in either habitat for the hybrid, the Carolina Chickadee and the Northern Chickadee have a narrow but very long range of interbreeding. And then there's the Liger and Tigon and Hinny and Mule where the female is sometimes fertile.
I would be flabbergasted (assuming elves were real) if any mammologist would classify elves (adulthood at 100 and lifespan of 750, darkvision, no sleep) and humans (adulthoodin late teens, lifespan under 100, regular vision, sleep) as the same species, even if the produce a hybrid (adulthood 20, lifespan 180 years, inferior darkvision, need sleep). Similar for orcs and humans. All in the same genus seems like a thing, perhaps as a ring species, if they actually had a common descent (which, for example, in Tolkien the elves and men wouldn't - what's the standard D&D origin?).