All three words relate to genes, but they differ in scope and register. 'Heritable' is the most precise scientific term, used specifically in genetics and medicine to describe traits or diseases that can be passed from one generation to the next. 'Hereditary' is the everyday equivalent — a doctor might tell a patient 'this condition is hereditary' in a consultation, while the same doctor's research paper would say 'a heritable disorder'. 'Inheritable' is a rarer synonym that appears mostly in legal or technical contexts rather than mainstream biology. 'Genetic' is the broadest of the three; it covers everything related to genes, including mutations that appear for the first time in an individual and are not inherited from a parent. For example, most cancers have a genetic component, but only about 5–10% are heritable.
From Latin 'hereditare' (to inherit), which comes from 'heres, hered-' (heir). The word passed through French into Middle English. The suffix '-able' was added to form the adjective, giving the sense 'capable of being inherited'.