The connection method
The last guy used the backstabs out of "necessity" (read: it was a "necessity" to use a 60 cent outlet instead of a $2.60 outlet that had screw-to-clamp terminals).
Follow Ed Beal's advice here, but with pigtails, that box will get rather crowded.
The box fill
As for practical fill, Ed Beal covers that very well.
Statutory fill rules are like this: A #14 wire counts for 2.00 cubic inches, a #12 wire counts for 2.25, and a #10 wire counts for 2.50.
- All cable clamps, together, count as 1 of the largest wire. 2.00 for you.
- All grounds, together, count as 1 of the largest wire. 2.00.
- Any "yoke" (that receptacle) counts as 2 of the largest wire attached to it. 4.00.
- Pigtails are free.
- Every other wire in the box counts as 1 of its own size. Your eight are 16.00.
Total 24.00 cubic inches. There should be a stamp on the back of that box indicating its cubic inches, 24 is pretty darn big for a 1-gang box.
If the box isn't big enough, get a "surface conduit starter box". This will stand up proud of the wall by an inch or so, but that will give you the needed cubic inches.
This is not a multi-wire branch circuit. This is two independent circuits on a single "yoke". Because of this, the two independent circuits must be handle-tied.
A handle-tie must come from the manufacturer of your breakers; you can't use a nail. While you're there, make sure your breakers are correct for your panel because there's no point buying a handle-tie for an alien breaker. If they are the same manufactuerer (Bryant=Cutler Hammer=Eaton), you are all set. Otherwise, they are probably wrong but ask.
Handle-ties are annoyingly difficult to find, and overpriced for being a bit of plastic. As such, some of us recommend using a 2-pole breaker instead - they are very easy to find for modernish panels, and they cost the same as 2 singles without having to pay for a handle-tie also.
The only difference is common trip (both shut off if one is overloaded): a 2-pole breaker guarantees this, a handle-tie does not guarantee it. For this purpose, we only need tied handles to assure common maintenance shutoff.