Urusei Yatsura uses lots of Japanese mythology as bases for the characters, namely the aliens. Here's a brief look:
Lum, Ten, Invader, Lum's Mother
Lum and her family are from the Oni race. In Japanese mythology, Oni are devil-like demons with long nails, wild hair, a fierce look and two horns. They wear tiger skins and can fly. During the time of the Japanese seclusion from the rest of the world and during war times, foreigners were looked at as Oni. Lum and her family wear tiger stripes, have horns, fly, and are unwelcome foreigners in Tomobiki-cho. More than fitting, yes?
Benten's name is that of the Japanese goddess of luck, and she is said to be based on Gong De Tian, the Chinese goddess of luck who is described as "in her left hand she holds a 'wish-fulfilling' pearl. With her right hand she makes a gesture of boldness." The pearl, no, but the boldness- yes. Benten is a tough biker babe who loves competition and gambling. After all, she is essentially Lady Luck.
Like Lum, Kurama is a princess - but of the Karasutengu, "crow goblins." Ten-gu are long-nosed, long-beaked tormenting spirits. Just as the karasutengu carry fans shaped like a large leaf and can summon wind, Kurama has a giant leaf she uses to make powerful gusts of wind.