For how the War started has been long gone due to the restructuring of everything for its first time, it can be considered that the war started by Prometheus sharing his flames to Humanity. This fire shared frobidden knowledge to which humans could gain from the Greek Pantheon. The gods didn’t like this and attempted to deal with Prometheus: he slaughtered them all. Shub Nighroth was about to get involved but Nyarlathotep assaulted her, while Lucifer and a band of angels who would be known as the Court of Goetias launched a rebellion against God.
The War was divided between two sides: Shub Nighroth and Elohim, with Lucifer and Prometheus on the other. Prometheus dealt with any Pantheon or council of Gods: whether it be Buddha, Gaia, or Shiva: none of them were a challenge for him and his horrific powers. The Children of Yog Sothoth were the only 7 beings who kept the war front plausible for Elohim and Shub. Prometheus during the war, created his own children to try and counter them: That being Mekhan, the God of Progress, Skay’r the God of Tradition and Triliath the God of Fate alongside the Anti God Superweapon known as the Anti King. Although powerful in their own right, his creations weren’t strong enough and through Shubs shattering of the Anti King, he would then turn to a more covert approach. Prometheus, seeing the Sixth Child, Abaddon to be the second youngest yet most naive began to tell lies: lies that warped his perception of things. This made the Concept of all Absolute Forces within Existence turn on his brothers: erasing Photinis and Umbarran; Brothers Light and Dark and scarring Athens for a time. If it wasn’t for Hydros and the Sub Reality he held, all would be lost. This however distracted Shub long enough to be executed by her brother Prometheus casually. Seeing his love die, Yog Sothoth took action for the first time in a very one sided battle. After a short scuffle, Yog Sothoth sealed his powers and trapped him inside the Outerverse itself.
In one last climatic battle: Elohim, nearly dead used the last of his powers to seal Lucifer into a prison he created: Hell. This turned Lucifer into a literal and figurative shadow of his former self. He and his allied rebels were now chained to conceptual Hell itself.
After the War, Yog Sothoth had to repair all the damages to Existence.