Then the problem could be that when you install the Oracle client the path environment variable gets set with the Oracle client path appended to it. It might be that the account you are using SSIS under does not have that in it. You can try appending the Path variable to include the Oracle client location and see if that resolves your issue. Here is an MSDN forum with a person who had a similar problem and their fix:

Running a SSIS package as a job error - with a connection to an Oracle database[/url]