I am currently in Canada and planning on claiming refugee status. My question is, if my claim is accepted and I apply for PR, can my parents and sister be included in my application and get PR visa to come here within a year or two? i.e can they come here as part of family reunification? my sister is 17 and she is dependent on my parents for financial support
No - you cannot include your parents or your sister in your application as dependents. You can only include your spouse (if you have one) and/or children (if you have any). Parents and siblings are not classified as dependents for immigration purposes.
You can qualify to sponsor your parents later (once you are a PR). However you should assume it will be at least four years from the time you become a PR until you can submit an application to sponsor your parents. It will take at least an additional 4 years for their application to be processed. So best case scenario, it will be a minimum of 8 years before your parents will have PR from the time you become a PR.