The Omni thing is hard to work out in a consistent way. Process Theism rejects it all together. I don't believe the term "maximally powerful" is used but I've seen the phrase "perfect power". Process Theism rejects the idea that God has absolute coercive power. If being is power, as accepted by many process theists, there can be no absolute power over other beings. God could only have Omni power if he was the only being in existence (say if all us were merely illusions and had no being of our own) but PT rejects that idea also. There was a book I was reading yesterday that discussed this idea; "A Platonic Philosophy of Religion, A Process Perspective.":
"In their ultimate individuality, beings, if they are instances of dynamic power, can be influenced by God, but they cannot be utterly coerced. As Hartshorne put the point, "power is influence, perfect power is perfect influence. Or again to have perfect power over all individuals is not to have all power. The greatest possible power over individuals cannot leave them powerless if being IS power Hence even perfect power must leave something for others to decide...
[quoting Hartshorne]:
'Power must be exercised upon something, at least if by power we mean influence, control; but the something controlled cannot be absolutely inert, since the merely passive, that which has no active tendency of it's own, is nothing; yet if the something acted upon is itself partly active, then there must be resistance, however slight, to the "absolute" power, and how can power which is resisted be absolute.'
If being is power, then any relation in which one of the related things was wholly powerless would be a relation in which "the thing" was absolutely nothing: an impossibility. No matter how lowly a thing may be, if it is a real individual it reacts upon things; cells, molecule, and electrons do not provide exceptions to the view of being as power."
Process Theism involves a panentheistic view of God and is a form of naturalistic theism***.
***
NATURALISTIC THEISM (from Charles Hartshornes webpage)
" A world of finite events exists necessarily, not through the arbitrary decision of the divine will. The existence of a plurality of finite experiences is as natural as God's own existence. The nature of the relations between God and the world is therefore a natural, necessary feature of reality. The
Hartshornean position hence says not only that every event has a creative power--[1] the power to shape itself in part, and [2] the power to influence future events. It
also says that the fact that every event has this twofold creative power is not simply a "fact," that is, not simply a contingent feature of our world. It is a necessary, natural feature of reality, not an arbitrary decree of the divine will that could have been otherwise and that could be overridden from time to time.
The presence of evil in our world and of every possible world is thereby explained. Evil results from multiple finite freedom, and any world God could have created would have had multiple finite freedom. The possibility of evil is necessary. No particular evils are necessary, but the possibility that evil can occur is necessary. . . . God does influence every event, but divine influence is always persuasion. It could not be unilateral determination.
. . . Freedom and danger necessarily rise proportionately. Because human beings have more freedom than other creatures, they necessarily are more dangerous and more capable of suffering. . . .Besides not determining the future, God does not even know the future, beyond those abstract features of the future that are already determined by the present. "
Seems like one of the more logical takes on theism to me. I'm still in the process of trying to take in and understand the philosophy and some of it's ramifications but I've been very impressed so far.