elder kings has several immortal variants
you have hagravens/brairharts, they do not die from old age/disease but you have a 50/50 chance of death when attempting and only hagraven cult members like this
you can become a vampire, wich also makes you immume to age/disease but makes ruling very hard due to opinion penalties
you can become a lich, wich again makes you immume to age/disease but you also become undead, making every non-undead hate you.
you can also become a proper immortal, wich is just called that, immortal. again immunity to disease/age and makes you infertile
Then there is "clone", wich is the exact same thing as immortal but you cannot do this yourself, it's used for dyviath-fyr's daughters
Each of these ways to become immortal is hard to obtain, usualy involves a high chance of death and some other requirements, most of the time you simply cannot do it.
Also, it does not make you a god, you can still be killed by other chars trough plot/war. orgnum starts as an immortal but you can execute/assasinate/slay him anyway.
The elves are technicly immortal, they age trough script otherwise they would not age at all! they do not die from old age either but they do lose health because of it, this makes them weak vs disease and that is the most common cause of death (besides being killed). Also elves have reduced fertility and issues making lots of children, even if you live 600 years (wich is not that hard) it's a miracle if you have 6 kids by then.