~PERSONALITY~
(Contains spoilers, so don't read if you haven't read the manga / watched whole the TV series yet. Or do read, but you've been warned)
Urd's personality developed constantly during the series, so it's quite difficult to describe.
At the beginning, when Urd arrives to Morisato residence, we see a really unpleasant person. She's pushy, arrogant, and doesn't think about anything but her own interests. She uses any methods to reach her aims, even if they harm others.
After being exiled to Earth she becomes a bit calmer, but still remains selfish and vain. She often teases and embarrasses people, even the ones she likes, let alone those who happen to annoy her.
After the events of the "Lord of Terror" Arc, where she has to face her dark side for the first time, we begin to see a somewhat different Urd, who finally develops some interest in the feelings of others. In fact, "Trials of Morisato" is just about the only time in the manga where we can see Urd be friendly and nice to a complete stranger, a boy named Shohei.
The next point that has a profound impact is "The Devil in Miss Urd" arc. She accepts the demonic half of her soul, but still insists, that being a goddess is incredibly important for her. After this she loses some of her selfishness and arrogance, seems less ashamed of displaying her concern for her loved ones, and, in genereal, becomes are more amiable person than she was before.
The latest chapters show her as a young woman who "just wants to have fun". She's relaxed, mischievous, likes playing tricks on others and teasing them. But at the same time she can be serious and caring when it's needed.