I fell asleep while reading a book. <-- correct, very natural I fell asleep over my book. <-- wrong "over" means "above" and you can't fall asleep above a book. Instead, you would use "on top of" meaning your head was on top of the book, touching the book as you slept. I fell asleep on top of my book. <-- correct I fell asleep over reading a book. <-- wrong I fell asleep with reading a book. <-- wrong

You set the context in your first sentence. While reading a book, you fall asleep. In that context, only the first sentence is natural. However if the context had been. "I woke up and felt something hard under me", you could say "It appeared that I fell asleep on top of my book". Otherwiseto answer your question, all the othe sentences are somewhat unusual

Actually over reading my book is a little unusual, but over can be used in a similar way. The child was so sleepy, they fell asleep over dinner. , Here "over" means "during".