Capo 1 for the original key
By "E6b" I mean E major with a flat 6th i.e. C natural

E                                           B7                Fdim   B7
So long, mom!                               And this is what he said on
I'm off to drop the Bomb                       E          Edim B7
   A         Am    E                        His way to Armageddon:
So don't wait up for me                     
A                                           E
But while you swelter                       So long, mom!
     E             C#7                      I'm off to drop the Bomb
Down there in your shelter                     A         Am       E
F#7                                         So don't wait up for me
You can see me                                  A        
B7                                          But though I may roam
On your TV                                            E            C#7
      E               E6b                   I'll come back to my home
While we're attacking frontally             F#7    
      E6             E7                     Although it may be
Watch Brin-k-ley and Hun-t-ley                B7
  E6        E6b                             A pile of debris
Describing contrapuntally                   
    A              G#7                      E         E6b
The cities we have lost                     Remember, mommy!
      A            E                            E6           E7
No need for you to miss a minute            I'm off to get a commie
       F#7          B7                      E6             E6b
Of the agonizing holocaust                  So send me a salami
Yeah!    E Fdim B7 x2                       A                   G#7
                                            And try to smile somehow
E                                                A
Little Johnny Jones                         I'll look for you
         B7                                          E      C#7
He was a US pilot                           When the war is over
And no shrinking violet                     
    E    Fdim B7                               F#7        B7        E        B7 E
Was he,                                     An hour and a half from now!            
E
He was mighty proud
               F#7 
When World War Three was declared
He wasn't scared
    B7
No siree!


Extra verse by foundring (youtube.com/watch?v=tVSi0DV_X3o). Just move the capo up to follow his key change.

E
So long, Dad!
I'm off to Stalingrad
   A     Am         E
So say a prayer for me
A
Stay safely at home
          E                  C#7
Streaming straight from your phone
      F#7
We'll make them retreat 
     B7
Each time you retweet 

     E              E6b
Just gimme one more brewski
E6       E7
And I'll bag another Russki
E6                          E6b
Though I never learned how to ski
    A                        G#7
Oh, you'll see we'll be just fine
   A          
No need to wait 
            E        C#7
I hear it's great to invade 
F#7                  B7             E
Mother Russia in the wintertime!