Yes, you stay in control of your posts. Open your post from the feed or from your profile, then use the post menu to delete it.
Once a post is deleted, it no longer appears in neighbours' feeds. Remember to remove posts that are no longer needed, for example once your give-away item has found a taker or your lost pet has been found.
If you posted something by mistake, delete it and then post a corrected version.
If a post won't go away, email us at contact@alleasyway.com.