So music like Yuki Kajiura - I talk to the Rain, where it has vocals but they are not any language we know of.
and songs like heart and courage
What you call such vocals depends on what genre of music you're in, but the term 'Vocalise' will cover most forms.
noun 1. a musical composition consisting of the singing of melody with vowel sounds or nonsense syllables rather than text, as for special effect in classical compositions, in polyphonic jazz singing by special groups, or in virtuoso vocal exercises.
2. any such singing exercise or vocalized melody. Compare like terms: doo-wop, melisma, scat singing, solfeggio.