The Christmas carol with the initials A I A M is "Away in a Manger". It was first published in the late 19th century, but it is not known for certain who wrote the lyrics. The first two verses were published in the May 1884 issue of The Myrtle, a publication of the Universalist Publishing House.
There are many different tunes used for singing the lyrics with the two most common settings being "The Cradle Song" by William J. Kirkpatrick and "Mueller" by James R. Murray.
Away in a Manger
While Shepherds Watched is a Christmas carol with the initials WSW.
It's a carol entitled, All my heart this night rejoices.
The Christmas song with the initials WIHIYS is Who Is He in Yonder Stall.
Nuttin' For Christmas.
Christmas angles
The Christmas song with the initials Z C is "Zither Carol". The song is a Bohemian/Czech Carol. There are at least two versions of the carol.
The real book that was made the Christmas carol
The Christmas carol with the initials DDMOH is "Ding Dong! Merrily on High."
in the bleak mid-winter
The song that contains the initials OLTOB is Oh Little Town Of Bethlehem.
A virgin most pure
Walking in the Air.