I'm sure if angels were meant to have souls Castiel would have been more interested in finding a stockpile of angelic souls instead of the souls of monsters for his war. Demons don't have souls because they are souls, and that is because they were once humans that had souls, the angels are a completely different race, where humans have a soul, they have grace.

Death is older than leviathan, angel and man, I doubt he has a soul since he predates the beings (humans) that were created to house souls. Nothing suggests that there is an afterlife for dead angels. If they had souls there would be an afterlife form them. I do recall death saying that soul can take far more than you'd expect, but nothing about it/he not having one itself. It's why Humans are valuable at all because Souls are so powerful a commodity. It's isn't stated so much that Death, Leviathans, Angels and the like don't have souls so much as Souls are uniquely Human so only Humans and human based creatures (Monsters, Demons, ect.) have souls. I believe it's mentioned around the time Sam is soulless and Death goes to the Cage to get his soul.