Yep, "Strangers in Paradise" is actually Polovtsian Dance. No.2 from the opera Prince Igor.

"All By Myself" and "Full Moon & Empty Arms" are the 2nd and 3rd movements, respectively, from Rachmaninoff's Piano Concerto No.2.

"Baubles, Bangles & Beads" is actually the Trio from a Borodin String Quartet.

No need for me to mention "A Fifth of Beethoven" or "A Night on Disco Mountain."

Part of the reason for so many of these songs have tunes drawn from Classical music is because of the rise of ASCAP made a lot of songs impossible to perform without the correct permission, so folks like the Dorseys & Tin Pan Alley began putting lyrics to Classical music to create copyright-free music to perform.