That's pretty rough.
The way my Dad taught me how to fit things together is to take it slow and fit, repeat as necessary.
Bedding compound will likely work well, as would epoxy or even JB weld, though nothing is going to make it pretty.
And forget about staining it.
One thing you may want to do if you do try to fill it, would be wrap the metal with saran wrap around the contact surfaces. That will make it so the filler will butt up to the receiver, but won't stick to it once it cures. You'll be able to peel the saran wrap from between the parts for a better looking joint without gluing them together.
It may be a better idea to start over with a different buttstock though if you're thinking about staining it or trying to make it look really pretty. Unless you're just wanting to get it serviceable of course, then it doesn't really matter what it looks like.
From the look of the notch, I would almost bet that buttstock came off of a different model gun altogether.