The producers were probably lazy on the music front. While they did put in some original scores, the four songs featured are not exactly new.
Theme Song: Utada Hikaru - Beautiful World (PLANITb acoustica mix)
A straight remix from the last release, they couldn't have got much easier than that. It is slightly better than the first version but that is it.
Shinji vs. Bardiel: 森山良子/Moriyama Ryoko - 今日の日はさような/Kyou no Hi wa Sayonara
A 60s pop hit that is better known as a graduation song or the Japanese equivalent of Auld Lang Syne. The juxaposition of a mellow tune with gory visuals is a good idea, however it did not work because there is not enough tension to build prior to that scene.
Shinji vs. Zeruel: 赤い鳥/Akaitori - 翼をください/Wings to Fly
The same idea, better executed. My rant is only because I don't like this song, it has been used in so many different productions that it had become stale and lame. Did I mention that even Susan Boyle did a cover?
Mary vs. Unnamed Third Angel: 水前寺清子/Suizenji Kyoko - 三百六十五歩のマーチ/March of 365 Steps
This is Mari's song as she drives Unit-05 forward; unfortunately it never made to the soundtracks due to copyright disputes. It belongs to the same league of j-pop standard of the previous two, however with some enka flair. My personal favorite, it effectively presents Mary's character in less than a minute.
Happiness does not fall from the sky
Therefore we must walk towards it
One step every day, three steps in three days
Three steps ahead, two steps back
Life goes like one-two punch
汗かき べそかき 歩こうよ
carry on with your sweat and tears
By the footprints you left behind
Pretty flowers will bloom
Shake your wrist, raise your feet
休まないで 歩け ソレ
Without a break, FOWARD!