I'm a teen so I may be able to help you out =]
Elizabeth - I know two Elizabeths. One goes by
Liz, and the other goes by
Lizzy.
Lizzy, within the past year, wants to be called
Liz. No teachers call her
Elizabeth, they both write
Liz on papers and everyone calls them
Liz.
Katharine/Katherine/Kathryn/Catherine - I know a
Catherine nicknamed Cat. Most Katherines go by
Kate or
Katie.
Julia - I know a
Julia that goes by
Jules. But that's just by her friends, not like an
Elizabeth going by
Liz, where you'd write it on papers and such. Some also call
Julia "
Ju" or "Jul"
Julianna - Same as above ^
Olivia - I have a neighbor named
Olivia [coincidentally her sister's name is
Catherine ^ from above!] and most call her Livi or
Liv. I also know another
Olivia and most call her
Livia. I personally like Livi.