Is it true that Oxxford usually quarter lines their jackets?
Yes; it's an Oxxford trademark.
Also, why is quarter lined more attractive than fully lined? I know that it may be "cooler," but personally I like a fully lined jacket. Maybe I've been brainwashed.
I like it for a number of reasons. First, to be perfectly honest, there's the snob appeal: I like the fact that the suits have a feature that most people wouldn't notice and wouldn't appreciate. Second, I like to be able to see the workmanship of the inside of the jacket (expecially Oxxford's bellows pockets), and the quarter lining. I think that the quarter lining makes the inside of the jacket look cleaner and more meticulous. Finally, there's obviously the coolness factor.