text: evangelical is different from evangelisch, but I do not know if that best applies.
  Maybe nondenominational?
  I spent too much time curious about this, to find ELAIA references, and:
  CZW sind eine überkonfessionelle, charismatische Versammlung.
  free_evangelical sees 65 uses,
  independent 55 times,
  and charismatic 34 uses.
  The connection to Israel does not turn up any frequent denominations in OSM, and I know too little about religion to be of much help.
  Perhaps a google-books excerpt returned from an Elaia keyword search:
     Die Mitgliedsgemeinden der Elaia Christengemeinden sind derzeit acht
     Gemeinden überwiegend charismatischer Prägung: die Ichthys Gemeinde ...
  as well as a description of beliefs I cannot find now, would cause me to tend to suggest charismatic, without knowing what it means ;-)