As it is, we have few hard numbers. The Alliance lost 50,000 dead in the war against the Lich King. But, IIRC, the Horde numbered only about a thousand warriors at Shattrath. A city like Stormwind in real life would probably be home to several hundred thousand people.
We've got a VERY rough feel for relative sizes.
Humans and Dwarves are populous, but humanity is still much reduced from its height.
There are likely lots of NElfs as they've managed to avoid the truly destructive wars.
The Orcs are split amongst planets and different Hordes.
The Tauren were described as being on the verge of extinction, thanks to the Centaur.
Same with the Draenei and BElfs and Gnomes
Worgen? I'd say they are quite numerous; but I'd also say many of them are feral.
Pandaren and Goblins - numerous overall, with tiny player populations.
Forsaken? Small but recently starting to grow.
Largest populations? Leaving aside player and NPC factions - Humans, Dwarves, NElfs, Orcs, Goblins, BElfs.
But those are guesses. In reality, the population sizes can be described as the size of plot.