I think you need to add date_request into the join criteria, otherwise your join does not generate unique results:
SELECT otd.userid,otd.task,otd.date_request,ot.approved_by
FROM otd INNER JOIN ot ON otd.userid = ot.requested_by AND otd.date_request = ot.date_request
WHERE otd.userid ='xxx'
AND CONVERT(varchar,otd.date_request,101) BETWEEN '09/10/2013' AND '09/11/2013'
AND ot.status ='A'
ORDER BY otd.date_request,ot.date_request ASC