What about Nicola as a first name? Seems to fit your requirements. It's lovely but I only know one under 20 and even she's 12ish.
I also really like Farrah and Callie.
Otherwise, strong but girly and not too popular:
Amy, Anna, Alexis, Abigail, Autumn, April, Amber, Ayla, Addison, Astrid, Aphra, Avery, Brooke, Belle, Bridget, Bryony, Bethan, Cara, Carys, Cerys, Claudia, Constance, Dana, Emma, Erin, Eden, Esther, Elise, Florence, Fallon, Giselle, Hannah, Harriet, Jocelyn, Juliette, Josephine, Jennifer, Kate, Kathryn, Lillian, Leah, Lois, Louisa, Miriam, Maria, Madeleine, Megan, Natasha, Philippa, Quinn, Rebecca, Rachel, Ruth, Rhian, Robyn, Rowan, Sorrell, Sadie, Sarah, Taryn, Tegan, Verity, Xanthe, Yasmin, Zara.