You emphasise something, but you do not emphasise on something.
For example: He emphasised the point that I made the other day.                        
                        He emphasised the importance of freedom from fear.
But you can lay emphasis on something.
                        For example: He laid emphasis on integrity.
So you emphasise something but lay emphasis on something.
The same applies to ‘stress’. You stress a point but you lay stress on some point. But you do not stress on something.
                         For Example: He stressed the importance of character.
                        He laid stress on the importance of character.