Wrong. Siren was non-elemental, status affliction silence. She didn't actually deal water damage, that was Leviathan.
Uh, wrong. Shiva, Ifrit, Ramuh, Leviathan, Titan and Garuda were celestials, from other worlds.
Fenrir, Diabolos and Carbuncle were Terrestrials, from Vana'diel, which made them more powerful than Celestials - though it should be noted in Carbuncle's case that his power was dwindling because of the effort required to keep Vana'diel safe. He was barely terrestrial level. Diabolos' power dwindled after the Shadow Lord became the Dynamis Lord also.
Odin, Bahamut and Alexander were actually gods.
Generally, Fenrir is way, way, way, way, way more powerful than Shiva. Just summoning him made Karaha-Baruha become a thing (which was no longer part of Vana'diel) and Sarutabaruta become a desert from the energy the summoning drew from the land, and later in wotg, two versions of Karaha-Baruha summoning Fenrir together resulted in the both of them dying.
Just sayin'
