In your SSIS packages, if you need to read from or write to Oracle likely that you most probably hit some Oracle Client related configuration issues. ORACLE_HOME, PATH environmental variables etc.
Sometimes you may see a machine needs to run SSIS packages and you see that an Oracle Client is installed but you don't know if the Oracle Client is 32bit or 64bit; and you want to know if it is 32bit or 64bit for some reason (Maybe a "Connection Manager" using Oracle OLEDB Provider is not passing "Test connection" in BIDS or this works but the package fails when you tried to run in SQL Job). Needles to say that all thos problems is a topic if your OS is 64bit.
The fastest way to understand if an installed Oracle Client is 64bit or 32bit, too look for "lib32" folder under ORACLE_HOME. If the Oracle Client is 32bit, it will contain a "lib" folder; but if it is a 64bit Oracle Client it will have both "lib" and "lib32" folders.
Hope it helps you sometime, someday :)