Vince, from your pictures, I don't see much if any oil soaking, but that would be a good thing to do. The thing I would be most concerned with is the wood near the broken part punky (soft)? If it is, then there is not much you can do as it will always be a weak spot.
I would use a good wood glue like Titebond III or a good two part epoxy for the glue-up, plus I would put a screw from the top tang slot on an angle to just behind the locks.
You can Acra-glas the stock after.
Your gun looks like it was dropped, as I have never seen one break like that from shooting.
If Dan May reads this he could help you out better.