According to Brian Jacques, as related in a live-action segment for the TV series:
> That was one of the Norse war cries, the Vikings, the sea-wolves, the Norsemen, and the Celts used to use it when they went into battle.
This is also stated in the Redwall FAQ:
> Eulalia is a Celtic/Norse battle cry which means Victory!!
This explanation has been noted to not match historical records, but it is the official answer from the author.