How should I repair a broken exterior PVC outlet body?
This is THHN wire in conduit.   I do conduit pipe repairs and conduit-body replacements all the time.   

That conduit body is not repairable.   

You cannot splice inside a conduit body.  They don't have the needed space.   Also you need 12" of slack to even think about a splice in a junction box.   

Mark and document

First, you make sure every wire is marked in a unique manner, typically by wrapping tape around the wires near the ends (both ends).  You may need to use diagnostic methods to suss this out, e.g. Unhook one white wire and see what loses power.  However in this particular case, it looks like your installer used a rainbow of wire, making this stupid easy.  This is why wire comes in 12 colors. 

Then you document where each wire goes.  Photos and colored tape helps. 

Easiest direction to pull

Then you decide which end has the fewest bends and will be easiest to pull.  Unhook all the wires and add a string to the mix, so you can pull the string through.  (it's not terribly hard to run a string through an empty conduit if you skip this step).  Pull them back to the defect point.  When they are near, wrap the bundle with tape, so they don't separate.   Pull off the string if  you added it.  When pulling with string, watch out for hot parts of your panel - this is why I don't like to do it.  Don't pull too hard, go back to the other site to correct any wire snags, so you don't rake the wire across a sharp edge. 

Make repairs.  Try to work around the ends of the wires, if you must pull/push them beyond the work area, try to do this absolutely no farther than necessary so you can grab it firmly with needle nose pliers.  Otherwise things get harder, you must pull it all the way out and do a "proper pull".  

Push and tease

Once repairs are complete, grab the wires.  Wrap the bundle  with wires staggered, starting at the first exposed wire end, to make the bundle as easy as possible to push through the conduit.  Bend the nose of the bundle so it doesn't hug the edge of the pipe (otherwise it will hang up on fittings). If you pulled a string through, add that string to the bundle, and pull.  Be gentle, if it feels like you might break the string, stop, and use the string to pull through a better string. 

Or I usually push them back the way they came.  This can sometimes be tedious.  The answer here is not force but finesse.  Force will only bend/crumple the wires inside the pipe.  I do about 90% of my pulls with this push-tease technique.  This will be easy until you hit the first bend, then harder.  It can be near impossible after two 90's.   I am not beneath temporarily disassembling a bit of conduit to help things along, but mainly, I build conduit with a lot of access points. 

If push-tease doesn't work, then break out the regular pulling tools - fishing tape, rope, bit of cloth and a vacuum cleaner, etc.