Is it possible to define package procedure/function outside of package body block (for Oracle)

This is happening because the division by zero error is being raised before the procedure is even executed - It's happening when the arguments are actually passed in to the procedure.

You can verify this with a small proc that doesn't do anything:

create or replace procedure do_nothing(divbyzero number)
IS
BEGIN
  NULL;
END;
/

Test:

SQL> exec do_nothing(1/0);
BEGIN do_nothing(1/0); END;

*
ERROR at line 1:
ORA-01476: divisor is equal to zero
ORA-06512: at line 1


SQL>

No this isn't possible.

A permanent TVF or view isn't an option due to the reference to #MyTempTable

I've seen a connect item request for temporary views and agree sometimes they would be useful. This was closed as duplicate of one requesting Module-level table expressions.

You might be able to rewrite as

SELECT A,
       B,
       C,
       CASE @calcType
         WHEN 1
           THEN sum(Amount)
         WHEN 2
           THEN avg(Amount)
       END
FROM   #MyTempTable t
       JOIN AnotherTable a
         ON t.Field1 = a.Field1
GROUP  BY A,
          B,
          C

Or if your needs were more complex (e.g. same shape resultset and using same source but different grouping conditions)

WITH Base
     AS (SELECT A,
                B,
                C,
                Factor,
                Type
         FROM   #MyTempTable t
                JOIN AnotherTable a
                  ON t.Field1 = a.Field1) 
SELECT A,
       B,
       C,
       sum(Amount)
FROM   Base
WHERE  @calcType = 1
GROUP  BY A,
          B,
          C
UNION ALL
SELECT A,
       B,
       C,
       CalcField = 0.0 * t.Factor
FROM   Base
WHERE  @calcType NOT IN ( 1, 2, 3 ) 

With the last one in particular you might consider OPTION (RECOMPILE) to simplify the plan. (Likely it would have a filter with a start up predicate without the hint and not actually execute the redundant branches but you would need to check. Also row estimates could be wrong with this approach if the startup predicate is retained).

If neither of those suited you would need to get into the realms of dynamic SQL.