mysql> CREATE TABLE `orders` (
    ->   `id` int(11) unsigned NOT NULL AUTO_INCREMENT,
    ->   `order_id` int(11) unsigned NOT NULL,
    ->   `name` varchar(255) COLLATE utf8_unicode_ci DEFAULT NULL,
    ->   `type` int(1) DEFAULT NULL,
    ->   PRIMARY KEY (`id`),
    ->   KEY `order_idx` (`order_id`)
    -> ) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE=utf8_unicode_ci;
Query OK, 0 rows affected (0.01 sec)

mysql> INSERT INTO `orders` (`id`, `order_id`, `name`, `type`)
    -> VALUES
    -> (1, 1, 'test', 1),
    -> (2, 1, 'test2-edited', -1),
    -> (3, 2, 'abc', 1),
    -> (4, 3, 'def', 1);
Query OK, 4 rows affected (0.00 sec)
Records: 4  Duplicates: 0  Warnings: 0

mysql> SELECT order_id, MIN(id) AS id, MIN(name) AS name, SUM(type) AS sum_types
    -> FROM orders
    -> GROUP BY order_id
    -> HAVING sum_types <> 0;
+----------+------+------+-----------+
| order_id | id   | name | sum_types |
+----------+------+------+-----------+
|        2 |    3 | abc  |         1 |
|        3 |    4 | def  |         1 |
+----------+------+------+-----------+
2 rows in set (0.00 sec)

mysql>