The problem of converting from any non-unicode source to a unicode SQL Server table can be solved by:
add a Data Conversion transformation step to your Data Flow
open the Data Conversion and select Unicode for each data type that applies
take note of the Output Alias of each applicable column (they are named Copy Of [original column name] by default)
now, in the Destination step, click on Mappings
change all of your input mappings to come from the aliased columns in the previous step (this is the step that is easily overlooked and will leave you wondering why you are still getting the same errors)