Well this is long to explain XD
If you notice, the kanjis for the spirits name have "numbers" in them :
Touka (十香 ) [十=10]
Yoshino (四糸乃) [四=4]
Kurumi (狂三) [三=3]
Kotori ( 五河) [ 五=5]
Yamai sisters (八舞) [八=6]
Miku (美九) [九=9]
Those "numbers" represent their position in the 10 sefirot.
http://en.wikipedia.org/wiki/Sephirot
Touka for example, is malkuth (kingship)
shown by her astral dress with armory designs
kotori, Gevurah (severity/strength)
shown by her position in the ratatoskr (commander)
yoshino, Chesed (kindness)
shown by her hesitation to attack the ASTs
Kurumi, binah has some relation with "left eye"
yeah, her left eye
and so on
Each sefirot has "angels" (probably, I don't know about these things well ><)
in DAL these "angels" are their powers
Touka : sandalphon
Yoshino : zadkiel
Kurumi : zafkiel
Kotori : camael
Yamai : raphael
Miku : gabriel
notice how everytime the spirits summon their weapon they shout those? those are the "angels"