Outlet giving off a burning smell
If you've replaced the outlet and are still getting the burning smell, then there is a serious fault in the wiring that needs to be corrected before you use the outlet again. 

Unfortunately, if the inside of the junction box and all the visible wiring looks good, then finding and repairing the fault could require tracing house wiring inside your walls, which usually means making holes in the walls1. 

But before you go that far, look inside all the adjacent outlet boxes, even the ones on the other side of the wall2. Outlets are often chained together and when one doesn't work it can be a fault in that outlet box or in the previous one. 

Be sure to call in professional help if you are not certain that you have found the problem. 

Please let us know how this is resolved. Many posters come here to ask about a fatally dangerous condition and are never heard from again. It makes me wonder how many people I've killed with my advice. 




Or just keep using the outlet, and eventually the fire department
will make the holes for you.
I know, you said the smell is just around the one outlet, but check
anyway.