That burned outlet looks familiar.... I encountered one like that about five or so years ago in a tiny house belonging to a church member with diabetes and MS.
The following loads were on the outlet:
5000 BTU window A/C unit (7.5A)
Pentium 166 PC with 17" monitor (2.5A)
Small washing machine (10A)
TV set & VCR player (1.5A)
OXYGEN CONCENTRATOR!! (5A)
Total load: 26.5A
Estimated continuous load: 12-17A
Now, this lady is dependent on O2, if the concentrator fails, she is in DEEP trouble. She does have bottled O2, but sometimes these run out. She calls me for all her electronics needs and she was complaining that her PC was rebooting..... after I found this she asked this: "oh, so would that have anything to do with the breaker tripping?"
The room was odd, it was a longish rectangle. In one corner was a hospital bed, directly across the room was the TV. At the corner near the foot of the bed was a washer/dryer combo that were unusually small (120V electric dryer...odd!). The PC was by her bed so she could check mail, surf the web and play scrabble. Under the bed was the burning plug! The wiring in the house itself was 12AWG plastic insulated romex and was in decent condition.
I redistributed the loads, got rid of a 18AWG extension cord in favor of a power strip with a circuit breaker and replaced that plug with a commercial grade one and side wired it.
I ended up replacing a lot of other outlets there.... all of them were a little loose and burnt in the kitchen with rather modest loads. The kitchen was upgraded from back stabbed plugs to side wired ones as well. The electrical problems were over for good from that day on. No rebooting PC, no hard to start A/C, no tripping breakers and no funky burnt smell. The microwave worked all the time too without having to "jiggle the plug".
