In PL/SQL the Boolean expression NULL=NULL evaluates to FALSE. : NULL « PL SQL Data Types « Oracle PL/SQL Tutorial

You need to wrap the selector in an NVL expression to be sure that it could never be NULL:

SQL> create or replace function f_getDateType (in_dt DATE)
  2  return VARCHAR2
  3  is
  4      v_out VARCHAR2(10);
  5  begin
  6      case nvl(to_char(in_dt,'d') , 0)
  7          when 0 then
  8          -- value will be null if in_dt is null
  9              v_out:='<NULL>';
 10          when 1 then
 11              v_out:='SUNDAY';
 12          when 7 then
 13              v_out:='SATURDAY';
 14          else
 15              v_out:='WEEKDAY';
 16      end case;
 17      return v_out;
 18  end;
 19  /

Function created.

SQL>
SQL>

21.24.NULL
	21.24.1.	All logical operations (including NOT) involving NULL always return NULL
	21.24.2.	variable:=nvl(value1,value2);
	21.24.3.	In PL/SQL the Boolean expression NULL=NULL evaluates to FALSE.
	21.24.4.	Short-circuit evaluation with conditional structures.
	21.24.5.	Compare with NULL value for equality
	21.24.6.	Compare with NULL value for non-equality
	21.24.7.	Compare NULL value and OR operator
	21.24.8.	Compare with NULL value and 'AND' operator
	21.24.9.	Compare Integer value with NULL value
	21.24.10.	Use IS NULL in IF statement
	21.24.11.	Use NVL in IF statement to deal with the NULL value comparison