I read a book, probably in the late 80s or early 90s, that had several elements. I remember enjoying the book then (it wasn't great art, but it was entertaining), but can't identify it now. The elements I remember was that there was a project called Trillium; there were two or three missiles with horrendous weapons that I believe were telekinetic and I think had American Indian names; the protagonist may have been a rock musician and also had some kind of psychic power. Any idea of the book name and author?
It's been a while since I read them, but might you be thinking of the series "The Tower and the Hive".
The series revolves around a family of "Talents" - people with telepathic and telekinetic skills, able to both communicate over interstellar distances, and to transfer cargo and ships over those distances.
Later novels in the sequence detail a war with "The Hive" which includes Talents posted on military vessels. These Talents provide various services, both supportive (bringing provisions from home, sending the injured home, even allowing people to take leave) and military (delivering missiles to their target with pinpoint precision).
Where the Tower and the Hive doesn't match your description is that the series has an ensemble cast, not a single protagonist.
The book you are thinking of is Star Fire by Ingo Swann. The Russian and American devices were the Tolkien and Tonopah respectively. I just thought about this book the other day and it was bothering me that I couldn't remember the name, so, the search was on. I am job hunting and Trillium Software is hiring. That got me thinking about the name Trillium and I thought it was an element mentioned in the Star Trek episode, "Devil in the Dark." "She(the Horta)thought your ears are attractive?" I'm still looking for that reference. Gotta love the internet.