The name of Elle's planet in Japanese is "Erusei". This is likely a pun on "urusei", part of the series title "Urusei Yatsura".
So you're Lum, the Oni-girl.
Lum: And you're Elle, the Darling-thief.
The opening credits show the residents of Tomobiki receiving invitations to the wedding and their reactions. There is also a scene featuring Lum chasing after Ataru.
In the original LD release, many early scenes were cut out: