Passing Comma Separated strings in SQL Server

You can create a table-type variable and pass it in as READ ONLY. It can be useful when you need array-like behavior from inputs. Unfortunately, you can't have a table-type output parameter.

create type dbo.CustomerIdArray as table (CustAccount int);

You could pass that into a procedure as READONLY and join to it as if it were a table. You'll need to alias it, because you can't use @ in the join syntax.

If you don't like the Table-type, and don't have access to a Tally/Number table, here's a solution that uses a common-table-expression to give you a Tally table which you can quickly use to separate a comma-separated string into rows on a table variable. You can then use the table variable in a join.

-- Here's your original string:
Declare @cust as VarChar(Max)
set @cust = '100031, 100131, 114647, 115101'

-- Declare Table variable to hold the rows of @cust
declare @TableOfCustAccount Table (CUSTACCOUNT int not null);

-- comma-separated values must begin and end with commas:
set @cust = ',' + @cust + ',';

-- Tally table CTE: add more joins if you don't have enough N values
;with Tally
as (
    select row_number() over (order by t1.column_id) as 'N'
      from sys.columns t1
      join sys.columns t2
        on 1=1
      -- You can get more N values by adding joins like this:
      -- join sys.columns t3
      --   on 1=1
   )
insert @TableOfCustAccount (CUSTACCOUNT)
select substring(@cust,N+1,charindex(',',@cust,N+1)-N-1)
  from Tally
 where N < len(@cust)
   and substring(@cust,N,1) = ',';

Now you can use @TableOfCustAccount as a join in your query.

There isn't a "list" data type in SQL, but what you can do is use varchar (or nvarchar) and dynamic SQL to accomplish what you are trying to do. For example:

Declare @cust as VarChar(Max)
set @cust = '100031, 100131, 114647, 115101'

DECLARE @sql as nvarchar(max) = '
SELECT
    DELIVERYNAME + '' '' + DELIVERYADDRESS AS ''Deliverly''
FROM
    dbo.SALESLINE INNER JOIN 
    dbo.CUSTPACKINGSLIPTRANS ON ORIGSALESID = dbo.SALESLINE.SALESID AND dbo.SALESLINE.ITEMID = dbo.CUSTPACKINGSLIPTRANS.ITEMID
WHERE
    CUSTACCOUNT in (' + @cust + ')
    AND
    dbo.CUSTPACKINGSLIPTRANS.CREATEDDATE BETWEEN ''08/03/2015'' AND ''08/07/2015''
    AND
    dbo.SALESLINE.DIMENSION2_ IN (''08'')
'

-- this is the query that was generated
SELECT @sql

-- this executes the query
EXEC sp_executesql @sql

I left the items in @cust as integers, but if you wanted them to be strings, you would have to include the quote literals when you set @cust.

There may be some concerns with SQL injection if this is something that is public-facing and gets the @cust parameters provided via user input.