Every God in the God of War universe, hold some sort of power, that makes them gods. These powers can be anything from summoning magic, to pure physical strength. Some powers can be used by the player if they kill the gods/goddesses. But to do so, they needs to pick up the source of the power from their bodies. This is because the player cannot learn magic just by killing. But they can use the gods items against them.
Such items can be, but are not limited to, Zeus' Gauntlets, Hermes' Boots, Hades' Claws, Thor's Hammer or even Odin's spear. By killing the god who holds these items, The player will be able to pick them up and use them as their own.
There are also gods or creatures that the player can kill and use a body part of theirs for their own gain and power. This can be for instance the head of Medusa, seeing as her eyes will still petrify her enemies even after being severed. But it can also be the head of Mímir which will still be alive once severed and his wisdom can be of great use to the player while travelling.