There's interesting and classy 'quirky', and then there's a bit naff 'quirky'. I think you have a few of both on your list.
GIRLS:
nova - I used to like, but is a bit 'teen mom' (as in the TV show, not a dig at teenage mums!)
piper - Pretty. Not that quirky though.
raven - It's okay, would only suit a certain type of person I think. I can't see it on a blonde haired blue eyed girly-girl, for example.
Harlow - Marlowe is much nicer and rarer and not a town in Essex
Elara - Not quirky, will blend into an ocean of 'el' names. Elowen is much prettier and classier
robyn - pretty. Not that unusual though if that's what you're going for. I know several.
xanthe - This name is very popular with Mumsnet! Not my taste, but nothing wrong with it
saxon - This is really bad. Saxon? Like Anglo-Saxon? Why?
lexie - Very, very popular and not at all quirky
wren - Gaining in popularity but a nice name. Very sweet.
kimberley - A bit dated.
zero - Zero? I wouldn't name a child this. Of all the numbers, 0? Like... Nothing. It's a bit sad.
khari - Is it pronounced like Carrie? If so, nice, but I prefer Carrie spelling.
iris - Very pretty but again, pretty popular
kaia - Nice. Popular in certain cultures. I know a lot of Turkish Kaias (but they're male)
tabitha - My daughter's name so I love it. Best one by far 
BOYS:
zakk - Zach is okay. Zack is also fine. Xakk is an awful spelling!
Harrison - Not rare or quirky
Lincoln - It's okay.
falcon - No! No! No! Falcon???
corey - No, very 90s.
phoenix - No, very 90s
jaxon - No, very chavvy
rex - No. I know 3 babies named Rex
Angus - Nice
hamish - Fine
blaze - No, a bit chavvy. Blaise is better.
ace - No! It sounds like a jokey nickname
brandon - probably the least quirky name I've ever heard 
wolf - So many babies recently named Wolf, Fox, Bear
zeppelin - Like... The thing?? The flying object? Why?
Zio - a bit nothingey
Balthazar - Cool, bold, biblical
styx - pronounced like sticks? Again, why?
toby - Another very un-quirky name 
patrick - Nice, not quirky
cooper - Fine, not quirky.
I don't like your boy's list much. The girls list is so much better!