DATEDIFF in HH:MM:SS format

You shouldn't be converting to time - it is meant to store a point in time on a single 24h clock, not a duration or interval (even one that is constrained on its own to < 24 hours, which clearly your data is not). Instead you can take the datediff in the smallest interval required (in your case, seconds), and then perform some math and string manipulation to present it in the output format you need (it might also be preferable to return the seconds to the application or report tool and have it do this work).

DECLARE @d TABLE
(
  id INT IDENTITY(1,1), 
  StartDateTime DATETIME, 
  EndDateTime DATETIME
);

INSERT @d(StartDateTime, EndDateTime) VALUES 
(DATEADD(DAY, -2, GETDATE()), DATEADD(MINUTE, 15, GETDATE())),
(GETDATE()                  , DATEADD(MINUTE, 22, GETDATE())),
(DATEADD(DAY, -1, GETDATE()), DATEADD(MINUTE,  5, GETDATE())),
(DATEADD(DAY, -4, GETDATE()), DATEADD(SECOND, 14, GETDATE()));

;WITH x AS (SELECT id, StartDateTime, EndDateTime, 
  d = DATEDIFF(SECOND, StartDateTime, EndDateTime),
  a = AVG(DATEDIFF(SECOND, StartDateTime, EndDateTime)) OVER()
  FROM @d
)
SELECT id, StartDateTime, EndDateTime,
  [delta_HH:MM:SS] = CONVERT(VARCHAR(5), d/60/60)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), d/60%60), 2)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), d % 60), 2),
  [avg_HH:MM:SS] = CONVERT(VARCHAR(5), a/60/60)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), a/60%60), 2)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), a % 60), 2)
FROM x;

Results:

id  StartDateTime        EndDateTime          delta_HH:MM:SS  avg_HH:MM:SS
--  -------------------  -------------------  --------------  ------------
1   2013-01-19 14:24:46  2013-01-21 14:39:46  48:15:00        42:10:33
2   2013-01-21 14:24:46  2013-01-21 14:46:46   0:22:00        42:10:33
3   2013-01-20 14:24:46  2013-01-21 14:29:46  24:05:00        42:10:33
4   2013-01-17 14:24:46  2013-01-21 14:25:00  96:00:14        42:10:33

This isn't precisely what you asked for, as it won't show just MM:SS for deltas < 1 hour. You can adjust that with a simple CASE expression:

;WITH x AS (SELECT id, StartDateTime, EndDateTime, 
  d = DATEDIFF(SECOND, StartDateTime, EndDateTime),
  a = AVG(DATEDIFF(SECOND, StartDateTime, EndDateTime)) OVER()
  FROM @d
)
SELECT id, StartDateTime, EndDateTime,
  [delta_HH:MM:SS] = CASE WHEN d >= 3600 THEN 
    CONVERT(VARCHAR(5), d/60/60) + ':' ELSE '' END
  + RIGHT('0' + CONVERT(VARCHAR(2), d/60%60), 2)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), d % 60), 2),
  [avg_HH:MM:SS] = CASE WHEN a >= 3600 THEN 
    CONVERT(VARCHAR(5), a/60/60) + ':' ELSE '' END
  + RIGHT('0' + CONVERT(VARCHAR(2), a/60%60), 2)
  + ':' + RIGHT('0' + CONVERT(VARCHAR(2), a % 60), 2)
FROM x;

This query changes the delta column in the 2nd row in the above result from 0:22:00 to 22:00.

I slightly modified Avinash's answer as it may end with error if difference is too big. If you need only HH:mm:ss it is sufficient to distinguish at seconds level ony like this:

SELECT CONVERT(time, 
  DATEADD(s, 
    DATEDIFF(s, 
      '2018-01-07 09:53:00', 
      '2018-01-07 11:53:01'), 
     CAST('1900-01-01 00:00:00.0000000' as datetime2)
   )
)

SELECT CONVERT(time, 
               DATEADD(mcs, 
                       DATEDIFF(mcs, 
                                '2007-05-07 09:53:00.0273335', 
                                '2007-05-07 09:53:01.0376635'), 
                       CAST('1900-01-01 00:00:00.0000000' as datetime2)
                      )
              )