Both OSC and M. use MySQL, right? Regardless of the "usualness" of the build, you can export into a text file and then import. Cells that contain data with lots of problem characters such as < " or line breaks can cause problems. Experiment with delimeters. This is very basic db stuff. But, a MySQL expert can automate it with commands. After the export and import is done, manually scroll thru all the tables for data integrity. No matter how big the db, I *always* randomly scroll through data to spot check. You'll learn a lot.
I'm in the process of evaluating a switch in carts myself. Can you tell me why you are switching from osc to Magento, please?