As more than one literary terminology educator has said, genre classification in literature is a subject that may prompt debate and conflict between critics and literature authors alike as it is certainly changeable and reliant on the tastes of the reading climate of the time. The Wednesday Wars gives a hint of how this may be true. Literature has major classifications and minor classifications. Classic literary divisions are derived from Greek classifications of drama (e.g., Antigone), poetry (e.g., The Iliad) and prose (e.g., Poetics). The fiction classification was added much later and comprises novels, novellas, and short stories. The recognized classifications in fiction are literary fiction and genre fiction.
According to the California Department of Education, the major divisions in genre fiction (excluding drama, poetry, and mythology) are fable, fairy tale, fantasy, folklore, historical fiction, horror, humor, legend, mystery, realistic fiction, science fiction, and tall tales. Other sources give the major genres as children's, fantasy, horror, mystery, romance, science fiction, thriller/suspense, westerns, and young adult.
There are also minor divisions under these major genre divisions (whichever list strikes your fancy) that are called sub-genres. Some sub-genres are adventure, African-American, coming of age, detective, gothic, and magical realism. There may be some controversy as to whether the divisions such as fable, fantasy, historical, and folklore are major genre classifications or sub-genres.
With this as the background, it will be understandable that The Wednesday Wars have been given a couple of different genre identifications. For some, the novel is Comedy and Humor with the sub-genre Historical Fiction. For others the genre classification is Children's Literature. For still others this novel is Coming of Age Fiction. Yet others classify it as Historical Fiction.
With all this in mind (and all the fine points about genre and sub-genre not herein included), it might be useful to give The Wednesday Wars a complex classification of Children's Fiction (for 9- to 12-year-olds) in the Middle or Junior Readers sub-genre that combines with the additional sub-genres of Coming of Age / Comedy and Humor / Historical.
It is Historical Fiction -- the Vietnam War era.