Moving electrical outlet 3 feet to the left
First, anytime you delete a receptacle or switch, you must review the minimum requirements for receptacles and switches.  You must not kill the only light switch in  the room, for instance, and you can't fall below the minimum spec for receptacle positions -- notably, any point along a wall must be (along-the-wall) within 6' of a receptacle.

12 AWG cable is the universal donor if you don't know what you're working with. 12 AWG is acceptable on both 15A and 20A circuits, the same places common NEMA 5-15 receps are allowed.  You must use the side screws or a screw-to-clamp feature; backstabs are never allowed with 12 AWG.  

Box fill

You won't make the cubic-inch problem any worse.  Officially you need 2.0 cubic inches per #14, 2.25 cubic inches per #12,  1 wire count's worth for all grounds, and if cable clamps stick into the box, 1 wire count's worth for all of them.  Then 2 wire count's worth for any receptacle or other type of yoke.  Pigtails are free. 

So that sounds like 9 x #12 == 20.25 cubic inches, or 6 x #14 + 3 x #12 = 18.75 cubic inches.  Most plastic boxes have that; but it will be molded into the back of the box normally, so go look.   

Besides, while you are adding two #12s, you're removing a yoke, which subtracts 2 wire counts. 

If you find yourself short on cubic inches, add a Legrand Wiremold "Surface conduit starter kit" which sticks out of the wall 1".  Stick an outlet there if you don't want it looking dorky. 

Nutting 4+

4 solid wires on a nut is not a problem; use the red nuts, square them up even, don't pre-twist, and twist like you mean it.  Then, give them a pull test - hold the nut and yank each wire in turn.  Fail the pull test = start over (don't cut) and refine your technique (line up better, twist harder).  Never use tape to solve a "failing the pull test" problem; failing means you have a bad connection which will arc and start a fire under load; tape helps you ignore it and adds kindling. 

You can even do 5 on a red nut if you need to put a receptacle back here.  They also make "screw-to-clamp" receps which allow 2 wires under each screw (so 4 per side). While backstabs are unreliable and #12 forbidden, these are reliable and #12-ok, if you torque them properly.