I can answer part of your question about Angela's Ashes. The book is so successful, in part, because the setting is Ireland, which has been a romantic favorite of readers for generations.
The songs, or anything specifically Irish, add realism to the setting, events, etc. This is an Irish story about an Irish boy, and songs contribute to the creation of the Irish society the narrator remembers. And that can only be good for readers. The narrator for most of the work is a boy, and the work for the most part is written in present tense to relate the immediacy of the narrative, as told by the boy. Songs are part of the experience, and they contribute to the Irish nature of the experience the boy relates.
A little more specifically, the enotes Study Guide on the novel says the following about related aspects of the novel:
The language used throughout is colloquial and earthy. Slang, Irishisms, and vulgar expressions are used frequently, and these convey the way people really talked in Limerick during the author's childhood. Having a ''fine fist,'' for example, means that a person has good handwriting. To go ‘‘beyond the beyonds'' is to behave in an outrageous manner.
I suggest the same can be said about the songs in the novel. They work the same as the slang, Irishisms, and vulgar expressions.