Oh, forgot Black Sabbath’s “Electric Funeral.”
Lehrer is the American standard, but for Britons, Flanders & Swann’s 20 Tons of TNT is equally remembered.
[ Yeah, mentioned it before. ]
Father, Mother, Son and Daughter,
Twenty tons of TNT.
Give us land and seed and water,
Twenty tons of TNT.
Children have no need of sharing-,
At each new nativity
Come the ghostly Magi bearing
Twenty tons of TNT.
I have seen it estimated:
Somewhere between death and birth
There are now three thousand million
People living on this earth
And the stock-piled mass destruction
Of the Nuclear Powers-That-Be
Equals-for each man or woman-
Twenty tons of TNT.
Every man of every nation
(Twenty tons of TNT)
Shall receive this allocation
Twenty tons of TNT.
Texan, Bantu, Slav or Maori,
Argentine or Singhalee,
Every maiden brings this dowry
Twenty tons of TNT.
Not for thirty silver shilling
Twenty tons of TNT.
Twenty thousand pounds a killing-
Twenty tons of TNT.
Twenty hundred years of teaching,
Give to each his legacy,
Plato, Buddha, Christ or Lenin,
Twenty tons of TNT.
Father, Mother, Son and Daughter,
Twenty tons of TNT.
Give us land and seed and water,
Twenty tons of TNT.
Children have no need of sharing-,
At each new nativity
Come the ghostly Magi bearing
Twenty tons of TNT.
Ends the tale that has no sequel
Twenty tons of TNT.
Now in death are all men equal
Twenty tons of TNT.
Teach me how to love my neighbour,
Do to him as he to me;
Share the fruits of all our labour
Twenty tons of TNT.
YouTube
Iron Maiden “2 Minutes to Midnight”
Weren’t, like, ALL of the songs by The Fixx about nuclear war? The three I can remember (“Stand or Fall,” “Red Skies,” “Are We Ourselves?”) all were.
And speaking of red skies, “Red Rain” by Peter Gabriel.
“Siberian Nights” by Twilight 22
So you believe everything you see
‘Cause you’re watchin’ the world on a color TV
You’ve got nuclear war, atomic rain
And nuclear war winter gonna freeze your brain, huh
That was one where people wondered whether it was about nuclear war or about acid rain.
Same with REM’s “Fall on Me.” Some thought it was about the proposed Star Wars missile defense system, some said it was about about acid rain. Could be either or neither, as with most REM songs.
The imagery was all over the place, but U2’s “Bullet the Blue Sky” may have been about a nuclear war.
My favorite Christmas carol EVER!!! 
Queen’s “Hammer To Fall” may not be officially about the threat of nuclear annihilation, but it is at least influenced by it.
And “War Pigs”, and “Children of the Grave” - buncha hippies, if you ask me.
Social Distortion’s “1945” is about the dawn of nuclear terror.
Too late to edit,(and I have to edit this) but: Why doesn’t Fear’s “Let’s Have a War” ever get mentioned? I know it’s not really germane to nuclear war, but I was wondering.
There was another novelty Christmas carol back in the '80s called “Red Christmas,” but I can’t find a recording of it anywhere:
Red Christmas!
The bombs are on their way!
HEY!
Red Christmas!
This must be the Russian way!
Tim Rose, Come Away, Melinda.
The Louvin Brothers - “The Great Atomic Power” (thanks to Uncle Tupelo)
Jefferson Airplane’s “House at Pooneil Corners”:
Suddenly everyone will look surprised
Stars spinning wheels in the skies
Sun is scrambled in their eyes
While the moon circles like a vulture
Some stood at a window and cried
‘One tear I thought that should stop a war
But someone is killing me’
That’s the last hour to think anymore
Jelly and juice and bubbles, bubbles on the floor
And Steely Dan’s “King of the World”:
When you come around
No more pain and no regrets
Watch the sun go brown
Smoking cobalt cigarettes
There’s no need to hide
Taking things the easy way
If I stay inside
I might live til Saturday
See post 26 for this and many like it
The Sun Is Burning by Ian Campbell
Fourth verse:
Don’t Go Down To The Fallout Shelter (With Anyone Else But Me) by Tom Fenton and Ice Nine.
A Dr. Demento favorite.
Shel Silverstein wrote two.
Standing on the Outside of Your Shelter https://www.youtube.com/watch?v=eZmrSVFIcyY
Drop the Bomb
…after a change of pace?
Both these songs don’t quite fit the thread, but are close enough IMHO, and I’ll probably never get another chance to share a couple of my favourite songs.
Kiwi classic reggae band Herbs with “Nuclear Waste.”
A song about the chemical spill at Bhopal by Tim Finn.