The composer who has won the most Academy Awards for original songs is someone who you might not expect. Alan Menken has several unusual stats to his name: he has won eight Oscars, more than any other composer.* He won the Oscar for this in 1991; two of the songs nominated that this one beat were also by him and Howard Ashburn, from this same film. Lastly, the Academy of Motion Pictures changed the rules of the game. Since Menken had won the Oscar in 1989 (The Little Mermaid), 1992 (Beauty and the Beast). and 1992 (Aladdin), they added an award for "Best Original Musical or Comedy Score" which was won by (wait for it) - Alan Menken in 1996 for Pocahontas.
Oh, yeah - he also has 11 Grammys, a Tony, and an Emmy. The's one of only 16 people to have collected each of the Big Four awards: Oscar, Grammy, Tony, and Emmy.
You might recognize some of this other music as well, notably Little Shop Of Horrors.
I'm not a fan of the recent Disney releases, but their films from the early 1990s were pretty spectacular.
* Alfred Newman, Twentieth Century Fox' music director won nine Oscars, but these were not for compositions.