Love In The Time Of Global Warming by Francesca Lia Block
Seventeen-year-old Penelope (Pen) has lost everything—her home, her parents, and her ten-year-old brother. Like a female Odysseus in search of home, she navigates a dark world full of strange creatures, gathers companions and loses them, finds love and loses it, and faces her mortal enemy.
Thanks to my friend Lesley for letting me know about the novel's cast being "chockfull of LGBT characters." Add your review of "Love In The Time Of Global Warming" in comments!