GROUP BY another table that have been grouped with two sub query

You have to use Group By to find val & val2 with duplicate values and need to use Inner Join and Left Join in order to include/eliminate records as given conditions (oppose to IN, NOT IN etc. clauses that might cause performance issues in case you're dealing with large data).

Please find the query below:

select t1.*from table1 t1 left join
      (select val from table1
       where val2 in (select val2 from table1 group by val2 having count(id) > 1)
        ) t2
 on t1.val = t2.val
 inner join
     (select val from table1 group by val having count(id) >1) t3
     on t1.val = t3.val
 where t2.val is null

Query for Reverse Condition:

select t1.*from table1 t1 inner join
       (select val from table1 group by val having count(id) = 1)
         t2
 on t1.val = t2.val
 inner join
     (select val2 from table1 group by val2 having count(id) >1) t3
     on t1.val2 = t3.val2

Please find fiddle for both queries here.

Excuse for any mistakes as this would be my first answer in this forum. Could you also try with below, i agree to the answer with window function though.

SELECT t.*
FROM   table1 t 
WHERE  t.val IN (SELECT val 
                   FROM table1 
                 GROUP BY val 
                 HAVING COUNT(val) > 1 
                    AND COUNT(val) = COUNT(DISTINCT val2)
                 )
AND    t.val NOT IN (SELECT t.val
                     FROM   table1 t
                     WHERE  EXISTS (SELECT 1
                             FROM   table1 tai
                             WHERE  tai.id != t.id
                             AND    tai.val2 = t.val2));

/* first part of where clause makes sure we have distinct values in column val2 for repeated value in column val

second part of where clause with not in tells us there is no value shares across different ids with respect to value in column val2 */

--reverse order query ( not sure gives the expected result)

SELECT t.*
FROM   table2 t
WHERE  t.val IN (SELECT val FROM table2 GROUP BY val HAVING COUNT(val) = 1)
AND    t.val2 IN (SELECT t.val2
                  FROM   table2 ta
                  WHERE  EXISTS (SELECT 1
                          FROM   table2 tai
                          WHERE  tai.id != ta.id
                          AND    tai.val = ta.val));

Can you try this and let me know the results? SQL fiddle

SELECT t1.id, t1.val, t1.val2 FROM table1 t1
JOIN (
  select val from
  (select id, val, val2 from table1 group by val2 having count(1) = 1) a
  group by a.val having count(1) > 1
)t2 on t1.val = t2.val;