Hey, I think you're making the problem worse by oiling the finished areas! The way that you avoid finish checking is during manufacture where the surface of the wood that's getting sprayed needs to be immaculately clean and oil-free so the varnish can properly adhere to the surface. You also need to pick a finish that expands and contracts in temperature and humidity changes compatibly with your body wood.
The classic cause of finish checking is when a cold instrument is warmed up too quickly - the finish and wood expand at different rates snapping the finish coating.
In your case, when you have cracks and oil it, you're contaminating the surface and probably causing the finish to let go even more.
I don't think you can undo this, but don't make it worse by putting oil on the broken finish!
Normally, I think you want to use oil only on the bare unfinished wood on your instrument - for a varnished instrument, that would only be the fingerboard. For the finished parts, you want to use a wax or polish to keep up the surface. Oil won't do any good there.
David Fung