Using the Angel Beats Wiki heavily, Yui seems to be based off YUI the Japanese singer. This is noted in the wiki in the Trivia section:
- Her back story seems to be a reference to Taiyou no Uta, a movie that the singer YUI starred in.
- The title of the episode Yui disappeared in is "Goodbye Days" which is also the title of the main song YUI sings in Taiyou no Uta.
Since YUI is a pop rock music artist, Yui may be based off the, punk, rock dress style. This can be seen in various aspects of here cloths:
- BDSM fashion, as she wears two halves of a handcuff,
- Fishnet like black ribbons,
- A chocker,
- Black boots, and
- Two cross-shaped barrettes.
Since punk rock was a rebellion against the system, and as they had transgressive sexual practices, some people wore more extreme fetish fashion, which Yui also has:
- Garters on both legs,
- 'Demon' wings and tail, and
- Cat teeth.
And so I think it's reasonable to assume she's based loosely off the punk rock style, which may be an easter egg about YUI being a rock artist.
An in-story explanation could be she wanted to dress however she wanted. This is as all, bar one, of her regrets are physical, which she couldn't do before she died (Angel Beats Wiki):
As the series progresses, Otonashi was able to fulfill her regrets. He helps her by doing the German Suplex, playing 5-on-1 soccer game (Maradona) and playing baseball (though she doesn't hit a homerun). After telling Otonashi that her last regret was marriage, Hinata later helps her fulfill her last regret by proposing to her, and giving her a vision of what could have been had they met in the real world.
Since she had to wear PJes since she was four till she was roughly a teenager, I think it's safe to assume she wanted a different, more expressive, change of cloths.