The four Heavenly Demons are part of the God of Death. There was no explanation given why the God of Death created four fragments of its soul but what Richard knew was that there are different ways of pleasing each of the Heavenly Demons.
The strongest Heavenly Demon—Ithryx gets pleased when more innocent people die.
Draeth loves seeing women and children wail in despair and die painfully.
Vornyx desires to see the blood of criminals.
And Thalvorn greeds for the blood beasts.
All of this makes up the population of all living beings, and if you try to please all the four demons, you would be making the God of Death stronger.
The one who cursed his mother and sister was Vornyx. And from what Allen said, the only way of curing them is,
"To summon the Great Lord Vornyx."
Richard frowned after hearing that. There is evidence which suggests that if you summon those of the residents of the Dark Star, one could get one wish granted.