TNSNames..... I feel bad for you. There are a couple things to try.
-Make sure tnsping works.
-The tnsnames.ora file needs to go in the network/admin folder. If it's in another location, it probably won't be found.
-Make sure the ORACLE_HOME path is set correctly.
Of course, if ODBC is working, then these are probably set up correctly. There are two other things to check for:
-Some searching revealed that SSIS might be running in 32-bit mode instead of 64-bit. If this is the case, then the 32-bit Oracle client will have to be installed and configured.
-If all else fails, you can try the Microsoft Connector for Oracle. 1.2 will work on 2008 and 2.0 will work on 2012. I haven't used it, but it's supposed to make integration with Oracle via SSIS easier.