Creatures from the legends of India.
Asura -- Elapatra -- Garuda -- Naga -- Naga Raja -- Rakshasa -- Rudra -- Rudran Baby -- Spirit Naga -- Water Naga
Asura is a Sanskrit word which was once used to refer to a certain group of Hindu gods (a variation also became incorporated into the name of Ahura Mazda, the "good god" of Zoroastarianism). Later on, the word was used to refer to enemies of the gods (often loosely referred to as demons). The asura myth had another overhaul when it was incorporated into Buddhism; one of the eight legions said to protect Buddha is made up of asuras, often depicted with six arms and three faces; the central face passive, the side faces angry. FF4's Asura is based on this look.
IMAGE: 8th century Japanese statue of an asura
A part-bird, part-man creature from Hindu belief, Garuda is represented variously as a man with a beak and wings, an eagle with human arms or other such variations. Im earlier legends Garuda was portrayed as a savage monster who served his mother, the demoness Diti. He was later seen, however, as holy; he was the mount of the god Vishnu.
IMAGE: Hindu picture of Garuda
Nagas are creatures from Indian legend which were human from the waists up and snakes from the waist down, and seen variously as demonic, flame-spitting monsters from the underworld or benevolent water spirits who bring rainshowers and guard springs.
Both the appearence of FF1's nagas (human-headed snakes) and the names "water naga" and "spirit naga" are taken from D&D, in which spirit nagas are evil creatures that hide in caves and attack passers-by and water nagas are, well, nagas that live in water.
Elepatra is one of the kings of the nagas, associated with the west. The other naga kings included Bindusara (east), Srimadaka (south) and Uttarmansa (north). "Raja" is a Hindi word meaning "ruler".
In Hindu mythology, rakshasas were shapeshifting demons that fought the gods. They came in a variety of forms, such as skeletons or bloated, deformed animals. Rakshasas were foolish creatures, and if a man pretended that they were related, the confused demon would leave him alone.
In Dungeons and Dragons, rakshasas are (clothed) humanoid tigers. This appearence most likely inspired the FF1 incarnation.
Rudra is a Hindu storm god, who later became regarded as a destructive aspect of Siva. His children are known as the Rudran (the plural of "Rudra").
As with a number of other mythological indivinduals, Square turned Rudra into a race of creatures (I'm assuming that the Rudra represents the original god, and the Rudran babies represent his children - calling a single creature by the plural word "rudran" is technically incorrect, but makes the mythological reference clearer). It also depicts them all as birds, which is understandable - as far as FF goes, it's not a huge leap from a storm god to a giant bird.
ASURA

GARUDA

NAGA, NAGA RAJA, SPIRIT NAGA, WATER NAGA, ELEPATRA

RAKSHASA

RUDRA, RUDRAN BABY
