Niki from Trulia here. I see that your profile is set up as a "renter" consumer type. In order to manage listings you must be a real estate professional. You can edit your profile if you are the property owner to be a real estate professional and choose "landlord" or "property manager" as the type.
To remove listings from Trulia, the update should be made in the "provided by" source site. If the listing was manually submitted there will be a delete option when you are in "My Listings" as a professional. If the listing was syndicated to us from another site, the status should be re-syndicated when the source site is updated.
You can also alert us to the status change as a consumer by flagging the listing in our site. We are happy to review the listing and make the needed updates to keep our data current.
Please feel free to contact us directly if you have more questions at firstname.lastname@example.org or by phone at 1-888-466-3501, Monday - Friday 7am to 4pm PST.