Question about putting in outlet w/ three sets of wire
Add a fourth wire to each set - that is 4-12" long.  I like 8-9".  Put the wire nut back on.  In fact, this is a good time to switch to red wire nuts if they're yellow. 

These short wires are called pigtails.  Attach them to the receptacle screws in the usual manner.     You can shuck down Romex or buy THHN wire, and you need one wire of each of these: 


Ground: MUST be green, yellow/green, bare, or stripped bare. (do not strip stranded wire bare; you'll get a birdsnest.)  
Neutral: MUST be white or gray. 
Hot: MUST be any unmentioned color. OR a white/gray wire with colored tape markings near each end.  


You can get all 3 from a white wire by stripping and remarking. 
If you use stranded THHN, the pushing into the box will be super easy, but attaching to the receptacle will be difficult. Consider screw-and-clamp type receptacles for that. 



I prefer to attach the pigtails to the receptacle first, and at a comfortable workbench. Then you only have to be in the awkward position for long enough to wire-nut.  I also put stranded on terminal screws, which is hard, so better  done at a bench.

Now, you have a big problem with cubic inches.  This box already has 6 conductors + 1 for all grounds; at 2.25 cubic inches/wire this box is already overfull. The pigtails won't add any (pigtails are free) but the  yoke (outlet) will add 2 wires' worth.    So let's give ourselves some more cubic inches in a tasteful way, using a Legrand Wiremold Surface Conduit Starter Box.  It's intended to surface mount and be a launch point for surface conduit, but it's good for just adding some cubic inches too.