In the Kabbalah (a theosophy based on the Jewish scriptures), there is a concept which is used to explain the different aspects of God. These aspects are called the sephiroth, sephirot, sefiroth, sephira, or sefira. This name means "ennumeration" in Hebrew. The sephiroth are often represented by a tree, the tree of life.
Cait Sith is named after a creature from Celtic mythology which can be called either Cait Sith or Cat Sidhe (pronounced cot shee). This name is a combination of the word "Cait," which means "cat" in Irish and Scottish Gaelic, and "Sidhe," which refers to otherworldly creatures. Cat Sidhe was a black cat with a white spot on its chest which lived in the Scottish Highlands. Some stories claimed that Cat Sidhe was actually a witch that disguised itself as a cat.
Stories of the Cat Sidhe most likely originated from sightings of a real creature, now called the Kellas cat. This rare species is larger than a domestic cat, but much smaller than what one would consider a big cat (like mountain lions and whatnot).
Wutai's name probably came from Mount Wutai in China, which Chinese Buddhism considers sacred - in addition to three other mountains. Each of the mountains represents one of the four great bodhisattvas (enlightened beings who give up nirvana for the sake of others). The four figures that are carved into Mount Da Chao in FF7 may represent these four bodhisattvas.
Also, the condition of Wutai in FF7 was highly reminiscent of postwar Japan, but I'm far too lazy to look that up and explain in detail. Maybe tomorrow.
