I want to learn the different shades of meaning and frequency of use of the following verbs that have the meaning of to die:
As suggested, here an extensive list, sorted by tone and kinds of death. There are several entries in the thesaurus which I am not familiar with – feel free to add them.
Kind of death:
Everything unmentioned is general purpose, with exception to self-inflicted deaths. In formal context (funeral, death announcement, etc.) all formal verbs turn to general purpose.
Only the following are applicable to self-inflicted deaths, e.g., suicide or Darwin Award candidate:
...And then there are the terms that describe dying of a specific cause:
If you refer to the death of a person in a formal context, like in an encyclopedia or newspaper article, you would most commonly use 'sterben' or 'versterben'. 'ableben' has the same neutral meaning, but it's far less common and rarely used in its verb form.
Animal deaths are usually referred to with 'verenden', but if it's a pet or otherwise respected/beloved animal, you would use 'sterben'.
Deaths of plants are always referred to as 'eingehen'.