Black smoke plus terrible odor means something in the TV got fried.

Why it is still working at all is the mystery.

Now, several days later, the TV is still working well. The odor has almost disappeared. The only change I notice now is fine gray horizontal lines in the background. This is new but not enough to bother me. It is, indeed, a mystery!

If it is a tube TV, there are three common failures with the storm and issues you describe:
If you ever decided to open it up and look...
1) flyback transformer - look for a suction cup looking thing stuck to the back/side of the tube itself and follow that back down to a black plastic box looking thing - see if that has any melted areas on it - if so I would stop using the TV
2) popped capacitor - usually in power supply section near where the power cord comes in - small usually blue can looking things - you will normally see a small metal plate on top with a scribed X - (about 1/4 the size of a dime) - if any of them are distorted or missing with black goo coming out they also smell bad and would be cause for not using the TV anymore
3) melted/blown power transformer - depending on the age of the TV - again cause to stop using it as a fire hazard.

Just some thoughts for you.
DF

Thanks. Just an update: yesterday, while I was watching a movie, the screen suddenly went black. The system totally died, even the DVD player. So, evidently the Nor'Easter power surge dealt its death knell. It was a 2001 Zenith.

lol, it could be from other sockets ,
other than the TV as TV is working perfectly ,
check the surroundings , pins , sockets and other gadgets present near the the TV.