Chapter 589: The Death of Asgard: Part VII

Oblivion has two main abilities that can be used either together or separately.

The first is erasure. 

By pulling people, objects, and even worlds into himself, they become forgotten about by mortals, monsters, and gods alike- and reality itself begins to re-write itself as if these things never existed to begin with. 

Once Abaddon 'rests' after erasing something, reality itself performs something like a hard save on a new game; permenantly erasing any and all traces of the lost individuals while creating new timelines without them.

Depending on the influence of the person, these changes to reality can be very little, or very big. 

And only outerversal beings and primordials would be able to tell that anything had changed. 

Oblivion's second ability lies within forgetfulness. 

Souls who were destroyed, even if not by his own hand, are sent to oblivion where they lament over the fate that has befallen them.