Wall outlet in house are burnt in wall
You'll have to move through each item and inspect it very carefully.  

Inspect and correct

Start with the junction box buried in the wall.  If that box is made out of any kind of plastic, or aluminum (not magnetic), or Magic Self-Burning Metal (magnesium, sodium, phosphorus, uranium, etc.), then the box needs to be replaced.  If it's made out of good old iron/steel, inspect it for serious arcing damage - if arcing has burned a hole in the box, it's done for.  Otherwise just scrub out the soot and call it good. 

Now the wires need to be viewed very critically. Manhandle the insulation.  If it is anything but resilient and strong, then the damaged insulation must go.    Now, look at what insulation remains.   Wires must extend  6" beyond the cable clamp, and, 3" beyond the surface of the wall, with only a modest amount (3/4") of insulation removed.  You can try loosening the cable clamp and see if you can pull more wire in.   If you still have the length, in good, undamaged insulation, and the metal wire is not discolored or polishes up easily... then you dodged a bullet and can continue the wire in service.  Otherwise the cable must be replaced.  Yeah, in the wall.  Ouch. 

As for the recep, carefully visually inspect it, follow with a borescope and X-ray -- I'm kidding, that recep costs 50 cents.  Just buy another one, except get the $3 kind that is better built.  

And use a torque screwdriver to set the correct torque on the screws. 

If any of the wires are aluminum, then use a recep rated CO-ALR.   Also, place an AFCI circuit breaker on this circuit.  If the circuit is not grounded (it might be via armored cable), then fit a combo GFCI/AFCI breaker, so you also have GFCI protection.  At your leisure, review all other outlets and ascertain if aluminum wire is present; if so, again use CO-ALR rated receps or switches, or Alumiconns, and torque correctly.   

Any outlets protected by GFCI may be installed as 3-prong.  Label them "GFCI Protected".  If they are not grounded, label them "No Equipment Ground". 



Now, move through the circuit and the house and inspect each other recep -  particularly ones that lost power, or that do lose power when this breaker is off.  Give them the same treatment as above, but see our Q&amp;A on what to watch out for when replacing receps.  

Next look at the service panel. Make sure all the breakers are the correct size for the wires they are feeding; 15A is pretty safe, no receptacle circuit should be over 20A.  Also look at what kind it is, and google whether this is a dangerous panel. (Hint: Pushmatic isn't dangerous, but it is obsolete).  If unsure, feel free to post a picture here.  (door open, no need to unscrew the cover; also get a shot of any labeling). 

What went wrong

Most likely a screw was torqued incorrectly, which is why they require torque screwdrivers now.  

Copper terminations have a serious defect in that they will not correctly clamp aluminum wire.  Many people used copper-only-rated receptacles with aluminum wire, and many more used devices rated CU-AL, a standard developed hastily and incorrectly by UL, and which proved to have severe problems and had to be revoked. 

It's also possible the circuit was wildly overloaded, but the breaker should have intervened to protect.  If it was a Zinsco or FPE firestarter panel, or a Pushmatic with Connecticut Electric breakers, that would explain why it did not.  It might also have been mis-sized; sometime when confronted with frequent breaker trips, idiots don't want to stop overloading the circuit, and instead put a larger breaker or fuse and let the wires smoke.  This is a mistake.