I think of a quirk as an unusual and unexpected character trait that someone holds firmly onto. Quirkiness to me is having a noticeable number of quirks.

Quirks as seen by muggles:
Carrying a pencil tucked above the ear
Ending most sentences with "haha"
Echolalia
Insisting on wearing purple and orange every day
Sticking tongue out while concentrating
Humming
Rocking in chair while reading
Using large words in uncommon places of conversation
Reading off time down to the second
Talking very fast
Quickly glancing of into the distance while talking

One or maybe two of those (or similar) is character flavor, more than say three or four is quirkiness.