The other queries are all going base on any ONE of the conditions qualifying and it will return a record... if you want to make sure the BOTH columns of table A are matched, you'll have to do something like...
select
tA.Col1,
tA.Col2,
tB.Val
from
TableA tA
join TableB tB
on ( tA.Col1 = tB.Col1 OR tA.Col1 = tB.Col2 )
AND ( tA.Col2 = tB.Col1 OR tA.Col2 = tB.Col2 )