Case is really only used when you are testing the same field over and over, so I think that you are in an IF situation.
IF(
ToNumber([Report Ready for Posting]) = 1 , "Posting" ,
ToNumber([Report Ready for Final Review]) = 1 , "Final Review" ,
ToNumber([Report Ready for 2nd Review]) = 1 , "2nd Review" ,
ToNumber([Report Ready to Review]) =1, "1st Review" ,
ToNumber([Report Ready to Process]) =1, "Report Processing" ,
ToNumber([Report Ready for LFee]) =1 , "License Fees" ,
ToNumber([Report Payment Data Received]) =1 , "Payments" ,
[# of Completed TSK]<2 , "Not Started", "some other default result")