This is all based on memory as I don't have the manga volumes to hand at the moment, but several of the songs were mentioned by title in the manga, and a few of them had lyrics shown that were used in the anime versions.
"Fuwa Fuwa Time" was in the manga, and we even see its lyrics in one scene when Mio hands her draft of the song to the others for feedback. If I remember correctly, "Watashi no Koi wa Hotchkiss" and "Fudepen Ballpen" are mentioned on the set list before one of the concerts. I believe that "Curry Nochi Rice" was also mentioned late in the manga, and I'm fairly sure the storyline where Yui first writes "Gohan wa Okazu", then writes "U&I" for Ui after Ui falls ill happened in the manga the same way it happened in the anime. I believe we did also see the lyrics for "U&I" when Ui finds Yui asleep at her desk after working on the song all night and looks over what Yui wrote.
The opening and ending themes were never mentioned or hinted at in the manga, and several of the other songs--e.g. "Pure Pure Heart", "Tenshi ni Nareta yo!"--were associated with anime-only plots. But a surprising number of the songs in the anime were actually mentioned by title in the manga.
Edit: I bought the digital editions and hunted down photographic evidence of my earlier claims.
In Volume 1, we see Ritsu and Sawako react with horror as they read Mio's draft of "Fuwa Fuwa Time".
In the background of the third and fourth panels on the left, we can see the first few stanzas of the song translated into English.
In Volume 2, Mio hands Ritsu a set list with four songs on it: "Fuwa Fuwa Time", "Curry Nochi Rice", "Watashi no Koi wa Hotchkiss", and "Fudepen Ballpen":
And in Volume 4, we see Yui write "Gohan wa Okazu":
Then later "U&I":
In Volume 4, we also get a few lines from a song that Mio was working on, which provokes the usual revulsion in Ritsu and Azusa:
At the end of the chapter, Ritsu declares that they'll develop a song around these lyrics in addition to "U&I" to spare Mio's feelings. However, I don't think there was any song in the anime based around these lyrics.