sterben is neutral and can be used for every kind of death. Also this is by far the most used.
ableben is a little bit elevated or euphemistic. It is usually used for quiet and slow deaths, i.e., by illness or old age. For example, this would usually not be used for somebody killed by an explosion.
versterben – if used in inofficial context: same as ableben, except for the euphemistic touch. If used in official context: same as sterben.
abtreten actually means to resign, to surrender one’s post or to exit. It is only used colloquially in the context of dying and at least with a grain of irony or metaphor.
erlöschen is only used for dying in combination with Leben.
Sein Leben erlosch. – He died.
krepieren has a disrespective note and also implies a painful or miserable death.
Krepier, du Schwein! – Die, you bastard!
verenden is usually only used for animals. If used for humans, this implies disrespect for the dying person.
eingehen is almost only used for plants and lower animals. I have never seen it used for humans.
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