Usage of "was having fun"

Hi,

Could you tell me which is correct?

  1. I was having fun while I read the book.
  2. I was having fun while I was reading the book.
  3. I had fun while I was reading the book.
  4. I had fun while I read the book.

Thanks a lot.
Liza

None of the sentences sounds natural to me. If I had to write it, I’d use “I had fun reading the book” or “I enjoyed reading it”