Evoke and invoke, two members of a small but powerful family of words relating to stimulus and response, have senses both similar and distinct. To evoke something is to call it forth, perhaps by bringing it to mind, or, synonymously with invoke, by summoning it (as in conjuration) or presenting it in support of an appeal (as when a rule or principle is invoked). Usually, invoke is used for the latter two meanings. The distinction is in the context; usually, something evoked is qualitative and intangible, whereas something invoked is material or practical.
Meanwhile, the related words provoke and revoke are also potent in their own right. To provoke is to prompt anger or an action (and is thus, in a limited sense, a direct synonym of evoke and invoke), while revoke means “to take back or recall.”
The root element common to this foursome, -voke, is an English form of the Latin stem voc-, from vox (“voice”), from which many words with the element voc-, such as vocal and vocabulary, are derived. (Voice itself is different in form because of its detour through French.) Another word with the voc- element is advocate, which means “to support vocally”; the noun form is identical.
The noun forms for evoke, invoke, and their cousins provoke and revoke are identical, produced by omitting the letters k and e and adding the ending -ation — resulting in evocation, invocation, provocation, and revocation — which correctly suggests that vocation and avocation also share an etymological origin (respectively, they mean, “calling,” as in what work one is called to do in life, and “call away,” as in an activity one engages in outside of work).
However, although avocados call to me, the word is unrelated; it’s from a Spanish alteration of ahuacatl, a word from the Nahuatl language, spoken by the Aztecs and by more than a million Mexicans. (I invite you to look up that word’s meaning yourself.)