~POWERS~
(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)
Lightning attacks
Urd's Bolt
Skysplitting Thunderblast
Depth Charge Advent
Blasting Photoelectric Attack Bullet
Lightning attacks are Urd's main weapon. She uses them quite often, even in minor arguments.
Fire Elemental Magic
As Urd's angel, World of Elegance, belongs to Fire domain, Urd can use Fire magic. We rarely can see it though, only in the chapter 89 of manga ("The Other Me"), its animated version from the TV series and in the movie.
Potions, pills and other medicines
Urd spends a lot of time in her chemical lab creating different potions and pills - love potions, truth serum, guts accelerator as well as true medicines.
Minimisation and splitting
Sometimes Urd splits into many small versions of herself. We can see it both manga and anime. Every mini-Urd is completely autonomous, and sometimes they can even go out of control (Adventures of Mini-Goddesses). She can also shrink in size without splitting, which seems to be a common ability among goddesses/demons.
Spellcasting and singing
These two seem to be also common abilities for goddesses/demons and Urd is good at both. She casts spells quite often in everyday life, while singing is a rare type of magic for her.