SSIS - getting "cannot convert between unicode and non-unicode string data types"

I am trying to create a SSIS package to copy one table in SQL Server 2005 to another table in SQL Server 2005. Both table have the same column definition (a varchar(50)). I am getting the "cannot convert" error. Beside sticking a Data Conversion task between the source and target, is there anything else I can do to get the package to work. I do not want to redefine any of the table columns to nvarchar.
I also want to do the same from Oracle (a varchar2(50)) to SQL Server 2005 (a varchar(50)). Is inserting a data conversion task the only way to make this work as well.
Thanks in advance for any and all comments/assistance.
Jethro.

Looks like you have some data which uses non ASCII characters. If so you can't convert unless you change them into another.

I am also getting this message; however, the table that the data is being extracted from and the target table both have the same collation: Latin1_General_CS_AI.
If I execute the SQL in a query tool, everything works fine but in SSIS it is not working.