Below are some recommendations I have of books featuring girls who are a different kind of "strong". Hopefully this inspires you to both read and write more layered heroines and to appreciate the undoubtedly strong girls and women in your lives!
Incidentally, a few of these are great diverse picks, too, so I'll be highlighting those as well. (Look for the "diversity alert"!)
girls who are strategists
(NOTE: The Winner's Curse is the first book of The Winner's Trilogy.)
(Diversity alert! Setting based on Spanish culture, most major characters are Latino/a.)
(Diversity alert! Setting based on medieval Japan featuring another country based on Africa.)
girls who find the silver linings in their "flaws"
Terra Cooper of Justina Chen Headley's North of Beautiful was born with a port-wine stain on her face. It's a prominent birthmark that mars everyone's view of her and even earns her the nickname "pretty ugly" from her own father. However, she comes to accept and even love herself over the course of the book. That takes a kind of strength that is quiet and universal, and I really admired that about this heroine.
girls who are technologically savvy
Maddie Brodatt from Elizabeth Wein's Code Name Verity (which I'm currently listening to as an audiobook) proves time and again that she can do just as well as - and frequently better than - the boys. She has the training and determination to go far, and her skills as a pilot, among other things, are recognized by even those who doubt her at first. Verity, the main character, is also a wireless operator and very good with both technological and interpersonal maneuvers.
girls who find strength in their relationships as well as their own selves
(Diversity alert! Setting based on Chinese mythology, plus girl/girl romance.)
Do you have any more suggestions? By all means, leave them in the comments! And go forth and enjoy these girls and these books!