How to remove non alphanumeric characters in SQL without creating a function?

If you have to use a single SELECT query like @Forty3 mentioned then the multiple REPLACEs like @Gordon-Linoff said is probably best (but definitely not ideal).

If you can update the data or use T-SQL, then you could do something like this from https://searchsqlserver.techtarget.com/tip/Replacing-non-alphanumeric-characters-in-strings-using-T-SQL:

while @@rowcount > 0
        update  user_list_original
        set     fname = replace(fname, substring(fname, patindex('%[^a-zA-Z ]%', fname), 1), '')
        where   patindex('%[^a-zA-Z ]%', fname) <> 0

Here is a starting point - you will need to adjust it to accommodate all of the columns which require cleansing:

;WITH allcharcte ( id, textcol1, textcol2, textcol1where, textcol2where )
     AS (SELECT id,
                CAST(textcol1 AS NVARCHAR(255)),
                CAST(textcol2 AS NVARCHAR(255)),
                -- Start the process of looking for non-alphanumeric chars in each
                -- of the text columns. The returned value from PATINDEX is the position
                -- of the non-alphanumeric char and is stored in the *where columns 
                -- of the CTE.
                PATINDEX(N'%[^0-9A-Z]%', textcol1),
                PATINDEX(N'%[^0-9A-Z]%', textcol2)
           FROM #temp

         UNION ALL

         -- This is the recursive part. It works through the rows which have been
         -- returned thus far processing them for use in the next iteration
         SELECT prev.id,
                -- If the *where column relevant for each of the columns is NOT NULL
                -- and NOT ZERO, then use the STUFF command to replace the char
                -- at that location with an empty string
                CASE ISNULL(prev.textcol1where, 0)
                  WHEN 0 THEN CAST(prev.textcol1 AS NVARCHAR(255))
                  ELSE CAST(STUFF(prev.textcol1, prev.textcol1where, 1, N'') AS NVARCHAR(255))
                END,
                CASE ISNULL(prev.textcol2where, 0)
                  WHEN 0 THEN CAST(prev.textcol2 AS NVARCHAR(255))
                  ELSE CAST(STUFF(prev.textcol2, prev.textcol2where, 1, N'') AS NVARCHAR(255))
                END,

                -- We now check for the existence of the next non-alphanumeric
                -- character AFTER we replace the most recent finding
                ISNULL(PATINDEX(N'%[^0-9A-Z]%', STUFF(prev.textcol1, prev.textcol1where, 1, N'')), 0),
                ISNULL(PATINDEX(N'%[^0-9A-Z]%', STUFF(prev.textcol2, prev.textcol2where, 1, N'')), 0)
           FROM allcharcte prev
          WHERE ISNULL(prev.textcol1where, 0) > 0
             OR ISNULL(prev.textcol2where, 0) > 0)
SELECT *
  FROM allcharcte
 WHERE textcol1where = 0
   AND textcol2where = 0 

Essentially, it is a recursive CTE which will repeatedly replace any non-alphanumeric character (found via the PATINDEX(N'%[^0-9A-Z]%', <column>)) with an empty string (via the STUFF(<column>, <where>, N'')). By replicating the blocks, you should be able to adapt it to any number of columns.

EDIT: If you anticipate having more than 100 instances of non-alphanumeric characters to strip out of any one column, you will need to adjust the MAXRECURSION property ahead of the call.