You have to enclose the OR part to brackets:
$sql = "SELECT ID,post_title,post_content,post_date,post_type
FROM {$wpdb->posts}
WHERE (post_content LIKE {$stuff})
AND post_status="publish"
AND post_type="{$post_type}"
AND ID != {$post->ID}
LIMIT {$limit}";
$results= $wpdb->get_results($sql);
Try this one:
SELECT ID,post_title,post_content,post_date,post_type FROM wp_posts WHERE (post_content LIKE '%Battery%' OR post_content LIKE '%Watcher%' OR post_content LIKE '%Widget%' OR post_content LIKE '%matches%' OR post_content LIKE '%built%' OR post_content LIKE '%HTC%' OR post_content LIKE '%widgets%' OR post_content LIKE '%Please%' OR post_content LIKE '%check%' OR post_content LIKE '%Thrutu%' OR post_content LIKE '%day%' OR post_content LIKE '%job%' OR post_content LIKE '%app%' OR post_content LIKE '%donate%' OR post_content LIKE '%buying%') AND post_status="publish" AND post_type="articles" AND ID != 1388 LIMIT 4