Hi Linday,
When you say stain, I assume you are talking about a light color coat over the entire piece. An antique finish, say. That, you would do after oilng. If you are talking about using a dye....then that should be done before oiling. Before you you dye, oil or antique, you should clean the leather with oxalic acid. This will help to remove and dirt or oils from handling which can affect how the the final color comes out. Really, we could use just a bit more info in order to better answer your questions.
Bob