Translation:I would be reading your book, but I have to work.
"I would be reading" makes no sense at all, it means "i'd read" as well and this one seems a better choice
In colloquial speech, we don't really say "would be reading" but I guess the translation is for the purpose of distinguishing czasownik dokonany vs niedokonany (perfective and imperfective verbs). It shows a clear contrast to "Przeczytałbym twoją książkę" which would be translated more as "I would HAVE READ (and finished) your book."
I disagree. This construction is used pretty frequently. Consider this conversation: "Are you reading my book?" "I would be reading your book right now if you'd stop talking to me!"/"I would be reading your book right now, but you won't stop asking me questions!"
We often say this type of sentence. In speech we typically use the contraction "I'd" instead of "I would". Is that what's confusing you? Consider these typical answers to the following question: "What would you be doing if you weren't here at work today?" I would be home watching TV. I would be sitting on a beach somewhere. I would be sleeping. I would be reading your book.
I suppose if someone asked "why aren't you reading my book?" I might reply like that, but it seemed unnatural otherwise. If I think of it as an answer to an accusatory question, it works, I didn't think of it as an answer.
I have to say that the Polish sentence isn't the best. "przeczytałbym" (I would read the whole book) is a lot more likely thing to be said. Well, maybe not in this sentence, as "Przeczytałbym twoją książkę, ale muszę pracować" sounds as if I was supposed to read the whole book in one sitting, which just isn't that common, but generally, one rather reads whole books.