Is it possible to convert a junction box with 4 sets of wires into a standard duplex receptacle
Yes, I see a big problem with crossed neutrals.  If the blacks are separated for some reason, the neutrals MUST also be separated.  

Nobody cares about the grounds being all together.  Unfortunately some people get carnal knowledge that all neutrals and grounds are in direct contact in the main panel, and that makes them tend to think of neutrals and grounds as the same thing.  That's not true at all.  Ground is a safety shield and power flows only during fault conditions. Current flows in loops and neutral is the other half of the loop!  

Thus, as Scott mentions, where the blacks are separated, the whites must be separated likewise.  

Could you put a receptacle there? Yes, but only if you also add a "box extension" there as well.  A typical box extension would be a Legrand Wiremold Surface Conduit Starter Kit.  

Since you have separated the hots and neutrals into 2 groups, place the receptacle on only one of those groups (hot and neutral pair).