Simplest solution: The Oracle client is not installed on the remote server where the SSIS package is being executed.
Slightly less simple solution: The Oracle client is installed on the remote server, but in the wrong bit-count for the SSIS installation. For example, if the 64-bit Oracle client is installed but SSIS is being executed with the 32-bit dtexec
executable, SSIS will not be able to find the Oracle client.
The solution in this case would be to install the 32-bit Oracle client side-by-side with the 64-bit client.