EMI Blackwood controls the song itself; certain performances and recordings will have their own protection.
Little Ruby Tunes.
Warner Tamerlane and Sony/ATV Songs.
You Be illin' is administered by Warner Chappell.
Myles O' Melody, and Happy Valley Music.
"Springtime for Hitler" is controlled by Sony/ATV in Nashville.
There are dozens of works by that title. The Mac Davis song, made popular by Elvis Presley, is handled by Sony/ATV; the Busta Rhymes/Rick James song is controlled by Jobete and administered by EMI.
As with most hip hop, there is a long list of stakeholders for each song, but most licensing can be handled through Universal.
Warner Chappell administers copyright of the song itself, but each performance and recording will have its own additional copyrights.
The song itself is in the public domain; however certain arrangements, settings, performances, and recordings may still be protected.
There are multiple copyright holders for each song, and rights in recordings would still be held by the labels. The organization you need to contact would depend on your intended use, and would still vary song by song.
Copyright covers written word only, but there are other rights over property such as recorded sound. The recording company owns the rights to the sound, and the recording company got the rights to the song lyrics from whichever songwriter copyrighted the lyrics themselves.
The number one Billboard song on February 2, 1956 was "Memories Are Made of This" by Dean Martin.