Since I have access to a local college's online library, I can view some e-books that have very good information.
I was able to view "Legacies of the Sword: The Kashima-Shinryu and Samurai Martial Culture" by Karl Friday
Warfare in early medieval Japan was deeply linked to the social structure. Examining the causes and conduct of military operations informs and enhances our understanding of the tenth to fourteenth centuries - the formative age of the Samurai.
A thorough and informative review, this study highlights the complex causal relationships between the structures and sources of early medieval political power, technology, and the conduct of war.
"The Culture of Civil War in Kyoto" by Mary Elizabeth Berry.
This has a big section having to do with the Onin War, however, it is very difficult to read. She seems to use too many big words perhaps in an attempt to flaunt her literary skill.
Nonetheless, both law and shogunal authority functioned best in support of prior negotiations about power, for medieval government retained the character of private accommodation. The shogun and his counselors, the great provincial families, and the local vassals of those families acted within a universe of mutual dependency whose members were variously ascendant and only fitfully aligned. A shogun's pronouncement about a family headship, let us say, might mean very little without the assent of both a man's peers and his formidable armed vassals. And in exercising the considerable prerogatives of his office, that head ruled successfully only when he balanced adroitly the expectations of lord, peer, and vassal.
"Yoshimasa and the Silver Pavilion: The Creation of the Soul of Japan" by Donald Keene
Has a fair bit of good information about the Onin War, and is much easier to read. However, it focuses more on the Shogun Ashikaga Yoshimasa than the participants in the war.
Forgive the formatting on the last one. But you can see it's a much easier, less dry read.
However, if anyone really wants to read about the Onin War, you might want to try "The Onin War: History of Its Origins and Background with a Selective Translation of 'The Chronicle of Onin'" by H. Paul Varley. However, the pricetag is hefty, usually costing $60.00-$80.00. It's often considered to be the best English source on the Onin War.
I'm buying my copy on Monday, and I don't mind buying the book because I plan on majoring in Japanese studies, and it will be a good source if I ever have to write about the war.
(Hope no one minds this off-topic chatter