How to ignore duplicate keys when extracting data using OPENQUERY while joining two tables?

I don't think there is a specific option. But it is easy enough to do:

insert into oldtable(. . .)
    select . . .
    from newtable
    where not exists (select 1 from oldtable where oldtable.id = newtable.id)

If there is more than one set of unique keys, you can add additional not exists statements.

EDIT:

For the revised problem:

insert into oldtable(. . .)
    select . . .
    from (select nt.*, row_number() over (partition by id order by (select null)) as seqnum
          from newtable nt
         ) nt
    where seqnum = 1 and
          not exists (select 1 from oldtable where oldtable.id = nt.id);

The row_number() function assigns a sequential number to each row within a group of rows. The group is defined by the partition by statement. The numbers start at 1 and increment from there. The order by clause says that you don't care about the order. Exactly one row with each id will have a value of 1. Duplicate rows will have a value larger than one. The seqnum = 1 chooses exactly one row per id.

If you are on SQL Server 2008+, you can use MERGE to do an INSERT if row does not exist, or an UPDATE.

Example:

MERGE
INTO    dataValue dv
USING   tmp_holding_DataValue t
ON      t.dateStamp = dv.dateStamp
        AND t.itemId = dv.itemId
WHEN NOT MATCHED THEN
INSERT  (dateStamp, itemId, value)
VALUES  (dateStamp, itemId, value)