There are many organizations in Azeroth and planetes beyond. Other than the alliance or horde.
The burning legion is a army of demons led by the fallen titan sargeras, mostly consisting of eradar and demons, they are based on the planet of argus, the dranei former homeworld. After sargerasas defeat at the hands of adventurers in the seat of the pantheon, the legion began to fall.
The old gods were ancient beings of void who were sent down by the void lords to destroy azeroth. forming the black empire, the current old gods are n'zoth the corrupter, yogg'saron, the god of death, y'sharri, the god of seven heads, and c'thun, god of madness and chaos. together, they were undefeated. That was until the titans came and sealed cthun, n'zoth, and yogg'saron away after seeing the monstrous results after the death of y'sharri, the titans made the decision to seal the old gods away. N'zoth was captured and detained underwater, in which he corrupted the highborne queen azhara and created the naga. Yogg'saron was captured next, being imprisoned within uldar in northrend, c'thun was caputered last, being imprisoned in ahn'qiraq.
Illadans forces were mostly formed out of illadari, naga, blood elves, and what remained of the dranei, now called the broken. All led by illadan, they strived to shut down all demon portals in outland. But akama, leader of the broken, betrayed illadan and aided heroes in the defeat of illadan at the black temple, and finally killed illadan.