Get AVG ignoring Null or Zero values

NULL is already ignored so you can use NULLIF to turn 0 to NULL. Also you don't need DISTINCT and your WHERE on ActualTime is not sargable.

SELECT AVG(cast(NULLIF(a.SecurityW, 0) AS BIGINT)) AS Average1,
       AVG(cast(NULLIF(a.TransferW, 0) AS BIGINT)) AS Average2,
       AVG(cast(NULLIF(a.StaffW, 0) AS BIGINT))    AS Average3
FROM   Table1 a
WHERE  a.ActualTime >= '20130401'
       AND a.ActualTime < '20130501' 

PS I have no idea what Table2 b is in the original query for as there is no join condition for it so have omitted it from my answer.

this should work, haven't tried though. this will exclude zero. NULL is excluded by default

AVG (CASE WHEN SecurityW <> 0 THEN SecurityW ELSE NULL END)

In Case of not considering '0' or 'NULL' in average function. Simply use

AVG(NULLIF(your_column_name,0))