One great thing about java and APKs is you can completely decompile the APK to java source code.
However, the resulting source coedcode isn't guaranteed to be identical.
One good way to try and match up the resulting source code with a known revision is to check what modifications were made directly before and after the known commit in the repository, and see if those modifications are also present in the decompiled source.
To decompile, use dex2jar and JD-Gui.
edit I just noticed you wanted linux tools. My only experience is with windows, but I'm sure similar tools exist for linux.