Hi Ahsan,
Yes, reports created in CR 2013 and CR 2011 should work fine in XI 3.1 or CR Server 2008.
It is however, recommended to have like versions of Server and Client tools which means you would need CR 2008 Designer for XI 3.1. So, you can open reports in the CR 2008 designer and save them so that their file formats change to 12.0. I'm assuming you can also create a .biar file for these reports and import them in XI 3.1.
-Abhilash