Even if your api uses oAuth I don't see how can you prevent the client app to steal the password.
At some point the user is going to have to give his password to someone. Can't the app ask the user for his password, keep it, and internally give it to oAuth to allow to use your api?
I meant for a native app and you being the provider. If you don't trust the client app even oAuth won't help you preventing the client app to know the user password.