Possible relationships between the gods and natural disasters:

Atheist interpretations:

1: Gods do not exist, and natural disasters have natural, impersonal causes.
2: Gods do not exist, and natural disasters are caused by human beings' collective subconscious (or perhaps even non-human animals' collective subconscious)

Deist interpretations:

1: God exists, but (s)he is not interested in human affairs, so the natural disasters still have natural, impersonal causes, and are not caused by God.
2: God exists, but (s)he is not interested in human affairs, and natural disasters are caused by human beings' collective subconscious (or perhaps even non-human animals' collective subconscious).

Monotheistic interpretations:

God causes the natural disasters, possible reasons?
1: To punish people for sin
2: Because God has mood swings, so (s)he causes destruction whenever (s)he feels angry or upset, but humans are not the reason for this anger, and they have done nothing wrong. God is just venting his/her anger into the physical world (s)he has created.
2.1: Humans can't do anything to placate God's anger.
2.2: Humans can placate God's anger in some ways. Some examples:
2.2.1: By offering a sacrifice to God
2.2.2: By praying to God
2.2.3: By praising God
2.2.4: By following specific rituals or behaviors

Duotheistic interpretations:

Types of duotheism:

Good/evil duotheism
Male/female duotheism
Strong/weak duotheism
Creation/destruction duotheism
Light/darkness duotheism
Mind/matter duotheism
Polarity duotheism

Good/evil duotheism (a good god and an evil god):

1: the evil god causes the natural disasters. Possible details:
1.1: The good god is omnipotent and can stop the evil god at any time, but (s)he decided not to, because humans have sinned, or for other reasons (such as... the good god didn't feel like stopping the evil god, for example)
1.2: The good god is not omnipotent, and (s)he needs prayers or offerings from humans to gain more power and prevent the evil god from causing more natural disasters. Or perhaps human kindness and generosity could empower the good god as well.
1.3: The good god is not omnipotent, and is less powerful than the evil god, so the good god cannot do anything to prevent the evil god from causing harm to humans. Possible details:
1.3.1: The evil god cannot be appeased by humans. The disasters stop whenever the evil god gets bored of causing disasters. The lack of disasters is always temporary.
1.3.2: The evil god can be appeased by humans through either sacrifices, prayers (to the evil god), by following specific rituals or behaviors, or by denouncing the good god.
2: Neither the good or the evil god cause natural disasters. Natural disasters have natural, impersonal causes. Possible details:
2.1: It is possible to convince the good god to reduce the amount of natural disasters and offer humans some degree of protection.
2.2: It is not possible to convince the good god to reduce the amount of natural disasters or to offer humans some degree of protection.

Polytheistic interpretations:

1: (Polydeism?) Gods exist but are not involved in human affairs, so the explanation is that natural disasters have natural and impersonal causes, just like in the atheist and deist interpretations.
2: Gods exist but they didn't cause the natural disasters (which have natural, impersonal causes), but gods can stop the natural disasters if they are given offerings, prayers, or even just kindness and generosity among humans.
3: Gods exist and they do cause natural disasters:
3.1: To punish humans for sin/impiety
3.2: Because the gods are angry for their own, but not because of humans (who have done nothing wrong), but for their own reasons, and to vent their anger they cause anger and destruction on Earth, and
3.2.1: Humans can't do anything about it.
3.2.2: Humans can appease them through offerings, prayers etc.
4: Gods exist but they do not cause natural disasters directly. Rather, the absence of the protector deities is the cause of the natural disasters. This view assumes that the default condition on Earth consists in very frequent natural disasters, death and misery, and the lack of natural disasters is attributed to the benevolent activity of the protector deities, who sometimes protect humans from the natural disasters (which have natural and impersonal causes, in this view). What causes the benevolence of the protector deities could be up to discussion.
4.1: The gods are omnipotent and their decision to withdraw their benevolence is their own decision.
4.2: The gods are not omnipotent and their power has to be fueled by humans in order for the gods to be able to give humans their benevolence, sometimes even if the gods want to give benevolence to humans, they are too weak to do that.

Interpretation of the theological view that says every human being contains a god or a goddess in their subconscious mind:

1: Natural disasters have natural, impersonal causes. They are not caused by divine subconscious activity.
2: Natural disasters are caused by divine subconscious activity. Some thoughts, memories etc. in the subconscious mind of humans can be the cause of natural disasters nearby, or somewhere else in the world.
2.1: It is possible to find some ways to tap into the subconscious of either an individual or that of the entire society and see if there's a way to reduce natural disasters by modifying people's subconscious.
2.2: It is not possible to enter the subconscious in a way that helps reduce natural disasters.