Study smth + a book

Yes, you can say that. You'll find some instances on this page.

Here are three of them.

(ref. 1) could be heard in their respective tents studying English from small guidebooks which they had brought along […]

(ref. 2) On the train going back home, I noticed a man studying English from a phrasebook.

(ref. 3) He remembers living in the Medina in Dakar , in a little shanty , studying English from a textbook he had bought […]

"I'm using this book to study English." is normal English. Both can be used in two contexts.

If you are being asked what you are doing with this book then you can say this.

• "I'm using this book to study English." (In speaking, you put sentence stress on "English".)

or

• "I'm studying English from this book." (In speaking, you again stress "English", even if is not the last word; this is so because the word that matters most in this context is "English".)

If you want to explain to someone how you study English you can use the same sentences, but in speaking you will not stress "English" this time; instead you will stress "book".