I want to make a web and native mobile application for android. My question is if doing a REST service served me for both, or would be more convenient to make a CRUD and a separate REST service. Is there any example and done with oauth REST? Thanks!

As far as I know, those acronyms mean 2 different things.

CRUD refers to the basic operations normally associated with an object - Create, Read, Update, Delete REST generally refers to a method of interacting with an application.