How can I repair and level the settled edges of a basement slab?
If you plan on using dri-core then you don't need to level the floor with self-leaving concrete or any similar method.  Instead, you'd just shim the dri-core panels to make them level.  

If you are just going to put down standard OSB then you'd want to use self-leaving concrete.

A big advantage to just shimming the dri-core is that most basement floors slope towards a drain and with shims, you'd maintain this slope so any water that gets beneath the dri-core would still drain properly instead of sitting underneath the OSB.  And of course this is why dri-core has a rubber bottom layer.