Nethys: the books actually disagree on whether He was mortal, if so whether He was one singular mortal or whether He's rather understood as the end-state of a process many mortals have undergone, and whether He actually counts properly as a god. If He was mortal, He probably became a god through doing a magic ritual which made Him able to see everything in the universe, which simultaneously made Him divine and fragmented Him into trillions of pieces and drove Him mad. Or maybe He broke into trillions of pieces and then some tiny fraction of them ascended. Or maybe He just saw into another plane where He was already a god and let that god possess Him but the process drove him mad. Or maybe, whenever someone seeks omniscience, they are added to Nethys, and that's why He's mad.
Hard to say, really.
Irori pursued mental and physical perfection. Gods were more perfect than mortals so in the course of becoming more perfect He became a god.
Erecura stole the secret of divinity from Pharasma, who punished her by sending her to Hell, or maybe Erecura literally was the secret of divinity, which grew a will of its own, or maybe Erecura just realized the secret of divinity in one of Her visions and then could not be separated from it, and took it with her into Hell seeking Hell's protection from Pharasma, or maybe Erecura foresaw that the secret of divinity would be needed in Hell, and took it there, defying Pharasma, or maybe Erecura is Pharasma's aspect of defiance and hubris, now acting independently from the rest of Pharasma somehow, or maybe Erecura is Pharasma's daughter after Atropos, or maybe Erecura is just a devil who made all that stuff up to make Herself more mysterious.