The MSORA is Microsoft's Oracle driver. There is not a 64bit version of the driver.
I would highly recommend using the Oracle's OLEDB driver when developing the package in BIDS so that you can utilize the Oracle driver on the server.
If you are loading data into Oracle, the OLEDB destination object will be very slow since there isn't a fast load option. Anything over 30K rows will be painfully slow, If you are using 2008 R2 you can utilize the new Oracle Connectors which has a fast load option. If you are using 2005 then you will need to look into using SQLLDR, an Oracle utility similar to BCP.