I think you're probably out of luck.
I believe there is an iCloud website you can go to. That will show you what you synced to the cloud.
As for recovering the data... your only hope is going to be one of recovery programs that simsaladimbamba mentioned. Or sending the drive to a data recovery company (but that's going to cost many hundreds of dollars or more).
The problem with the recover is that it is easy to recover a deleted file (or partition in your case). It is not easy to recover a deleted file AFTER new data has been written to that part of the disk.
When you re-installed OSX, you most likely wrote over some (or all) of the disk sectors that used to contain your data.
It is still possible that you can recover some of your data with one of the recovery programs.