Deleting from the database
They can't be found in FTP, because they're in the database only. However, if they're not found in the admin area, but still show up on the blog, I'd try the following:
1.) You sure they're not showing up in admin? Go to Posts->Edit, and check each page. That view only shows 15 posts at a time, so it may be on a back page. Sorry if this seems insultingly simple, but people miss stuff sometimes, just like how we've all experienced searching earnestly for the carton of milk sitting at eye level in the front of the fridge.
2.) Go to the Plugins page and see if WP-Cache or WP Super Cache is installed. If so, go to Settings->WP Cache (or Settings->WP Super Cache) and hit the "Delete Cache" button. Go back to the blog view page (i.e. not the admin area), reload it, and see if the posts are still there. You may just have a bad version of the blog cached.
3.) If all else fails, we can wipe the posts directly from the database. You probably have phpMyAdmin on your database server (most webhosts do.) Navigate to your phpMyAdmin page, and open the database for the Wordpress installation (it will contain at least 11 tables.) Click the posts table (called wp_posts by default -- if you specified a different prefix, like xyz, it'll be called xyz_posts instead), then click the Browse tab. Find the post you want to kill, and click the red 'x' next to it. Before you do this, make a note of the post_id column's value.
Note that #3 will result in a minor integrity violation in your database. Under normal circumstances, this is harmless, though if you run a cache plugin, you'll want to do step #2 again after doing step #3. If you really want to fix the integrity error, though, click the "SQL" tab and enter these two lines:
delete from `wp_comments` where comment_post_ID=123;
delete from `wp_postmeta` where post_ID=123;
Note that wp should instead be your prefix, and 123 should be that post_id from step #3. There may be some other detrius in the database depending on what other plugins you run, but if the plugins are written correctly it shouldn't do any harm.