Ellen Raskin's The Mysterious Disappearance of Leon (I Mean Noel) is one of the weirdest books I've ever encountered. It involves a woman who wears the same outfit for years and years and years so on the off-chance that the man she once "loved" comes back, he'll recognize her. That sounds chick lit-y. It's not. See, the woman was also an heiress to some soup business and was married at age 5 in order to keep it in the family. The last message she has from her husband was heard whilst he was drowning, so it's obscured by "glubs" and blubs." She spends the majority of her lifetime trying to solve the puzzle of this message to find his whereabouts and get on with their lives together, with the help of her friend and twins she adopts. So there's soup, glubs, blubs, word puzzles, changed identities, and just a whole mess of weird randomness. It's lovely.
Raskin also wrote The Westing Game which, in the words of my fellow Children's Literature and Media classmates, is "THE BEST BOOK EVER," so I never doubted that this book would be just as great.