I leave the question open whether one takes them in a weak sense (where it is seen as some element in a theodicy) or in a stronger sense (where it is seen as constituting the whole theodicy)
1.) Permission is Creation. God’s “permission of evils” means that he has created something other than God, and for anything fitting this description evil is a logical possibility. The existence of the universe is the greater good for which evil is allowed. There is no subsequent act of allowance after creation, only a creation in which evil is a logical possibility and so never could be ruled out.
2.) Permission for possibility. God allows some evils because they make a subsequent good possible, but that subsequent good might very well not come to pass. If this “not coming to pass” is in turn seen as another evil allowed, it might lead to a regress of missed opportunities that might coalesce and find resolution in incalculably complex ways.
3.) Incarnational permission. The Incarnation is understood as a good capable of justifying an infinite or all but infinite amount of evil, which ultimately are to be reversed entirely and in no other way than by the action of the Incarnation in the world. Evils are seen more or less generically, not as any one in particular as leading to Incarnation, even if Incarnation is ordered to reversing all in particular.
4.) Competing value permission. Goods and values are implicated in one another in such a way that we cannot maximize any one. The features that make a house attractive are also to a large extent exclusive (affordability, size, location to good neighborhoods). As Anselm points out to Guanilo, finite goods are never able to attain a maximal level of all possible goods. This is true just as much for any one being as for an aggregate of beings. Perhaps some person, just as some value, just has to get the short end of the stick.
In writing this, however, it’s hard to avoid the idea that theodicy as such arises from a poorly framed question or a failure to get the point. Our existential situation is not one where, in the face of evil we demand that God give some account of himself, but of needing God in order for the evil to have any meaning. Our most vexing evils are either bad luck or our own bad choices (wrong place, wrong time, wrong choice) and only a god could make any of this work out.