The type of a case statement is determined by the first clause in it. In this case, the first clause is a varchar string rather than an nvarchar.

Try this:

UPDATE TableA t
    SET t.Last_Col = (CASE WHEN t.First_Col = N'ItemOne'
                           THEN N'anItemOne'
                           WHEN t.First_Col = N'ItemTwo'
                           THEN (CASE WHEN t.Second_Col = N'ItemTwo_A'
                                      THEN N'aSecondItem_A'
                                      ELSE N'aSecondItem'
                                 END)
                           ELSE N'NoItem'
                        END ); 

Labels: noteToSelf, oracle