Order By with Case Statements Not Working as Expected - sql-server

Question

I'm trying to sort a report in the order that the end user wants to work it.
First, it should be sorted by the following scenarios:
String_Field is populated, but Comment_Date is null
String_Field is not populated
Both String_Field and Comment_Date are populated
And then it should be sorted by the aging of Task_Date.
I've added the following to my ORDER BY:
(case when max(table1.comment_date) is null then 2 else 1 end) DESC,
(case when table1.string_field is null then 2 else 1 end) ASC,
max(table2.task_date) ASC
And then I added them to my SELECT also:
(case when max(table1.comment_date) is null then 2 else 1 end) as sort1
(case when table1.string_field is null then 2 else 1 end) as sort2
max(table2.task_date) as task_date
What I'm getting, and cannot figure out for the life of me why, is this (edited to show the high/low at each change):
I've tried casting, moving the aggregation around, and adding the values together, and I still end up with those 2s stuck in the middle of some invisible split in the 1s.
If it makes any difference, I come up with the values for string_field via a CTE Union Query, and comment_date is joined to string_field in a second CTE, before the second CTE (table1) is left joined to the table that contains task_date (table2). You can have a string_field without a comment_date, but never a comment_date without a string_field. There must be a task_date for the entry to appear in the report. The report is grouped by string_field.
I'm on SQL Server 2008 R2.
Thanks in advance for your help!
Edited to add Quasi-SQL:
WITH
old_new_string AS (
SELECT
tablea.old_string_field,
tablea.string_field,
'A' as match_type
FROM
tablea
WHERE
tablea.old_string_field is not null
UNION ALL
SELECT
B1.string_field AS old_string_field,
B2.string_field AS string_field,
'B1' as match_type
FROM
tableb B1
INNER JOIN tableb B2 ON B1.string_field <> B2.string_field AND B1.id1 = B2.id1
WHERE
B1.id1 is not null
UNION ALL
SELECT
B1.string_field AS old_string_field,
B2.string_field AS string_field,
'B2' as match_type
FROM
tableb B1
INNER JOIN tableb B2 ON B1.string_field <> B2.string_field AND B1.id1 = B2.id2
WHERE
B1.id1 is not null),
table1 AS (
SELECT TOP 100 PERCENT /* Enables order by to improve join performance */
old_new_string.old_string_field,
old_new_string.string_field,
old_new_string.match_type,
comment_date = (SELECT max(comment_table.comment_date) FROM comment_table WHERE old_new_string.string_field = comment_table.string_field and comment_table.comment_code = '001')
FROM
old_new_string
ORDER BY
old_new_string.old_string_field)
SELECT
tablez.string_field as old_string_field,
max(table2.task_date) as task_date,
min(cast(getdate() - table2.task_date as bigint)) as Aging
table1.string_field as new_string_field,
max(table1.match_type) as match_type,
max(table1.comment_date) as comment_date,
sort_order1 = (case when max(table1.comment_date) is null then 2 else 1 end),
sort_order2 = (case when table1.string_field is null then 2 else 1 end)
FROM
tablez
INNER JOIN table2 ON tablez.string_field = table2.string_field
LEFT JOIN table1 on tablez.string_field = table1.old_string_field
Where
table2.task_date IS NOT NULL
Group By
tablez.string_field, table1.new_string_field
ORDER BY
(case when max(table1.comment_date) is null then 2 else 1 end) DESC,
(case when table1.string_field is null then 2 else 1 end) ASC,
max(table2.task_date) ASC

Answer 1

ORDER BY
case when max(table1.comment_date) is null then 2 else 0 end
+ case when table1.string_field is null then 0 else 1 end DESC
or
ORDER BY CASE
WHEN max(table1.comment_date) is null and table1.string_field is not null
THEN 0
WHEN table1.string_field is null
THEN 1
WHEN max(table1.comment_date) is not null and table1.string_field is not null
THEN 2
ELSE 3 END