Divine Form - Avatars of the Deities

On their home plane of existence, you could interact with a deity in a physical form. This is not practical for a living mortal, if your lucky you will gain admittance when you pass on from this world. Thus, the normal way to interact with your deity is through prayer. It is also said that a deity can communicate to multiple people having a near-infinite amount of conversations at one time.
If, however, a deity wanted to make a point, they would not come as a voice or vision. In days long gone if the deities would physically interact with mortals the deity would take a physical form, as one of its avatars. This form was more limited, but also more impactful.
While the deities could appear as any creature, animal, or beast most have a preferred form that they will take, an echo of what we painted them as. In such a way some deities take different forms to their followers. Forms that make them appear as Human, Dwarven, or Elven. Many theological debates have been fought over the deities and their true form.
While the deities can appear anywhere, they will normally appear where the domains are at the strongest. This is based on their connection to a domain. A domain steeped in the power that grounds the deity is simply easier to maintain form within and takes less of their attention.
Deities despite this are not all-powerful. They will tire and can be overpowered by other immortals. If they were to choose to take place in a physical battle in this realm their avatar form can take physical damage. From mere mortals with the proper weaponry and powers, a god can be worn down, not killed. If an avatar takes enough damage it will be banished for a time as it reforms in its home plane of existence.
Since a deity that extends its energy to form an avatar takes energy and concentration. That energy is bound to the avatar and limits what else the deity might do at the same time. Only a very powerful deity can be in more than one place when in avatar form.
To truly damage a deity a mortal would need to wear the deity down until it was near death but before it is banished. They would then need to bind the deity so that it can not escape. Make no doubt, that this is a near-impossible task. If weakened and bound in a container that can hold the essence of a deity. You would need to remove the container from the domain(s) from which it draws power from.
If all this were done, the deity would slowly weaken. Then and only then it would be theoretically possible to shatter the binding vessel and separate it far enough away for it to not reform, thus killing a deity.

See Also

The Divine Gate .:. Ritual Investiture

Divine Energy

Deities exist on pure divine energy. They can draw power from and control their sphere(s) of power, the things they have dominion over. These domains can be small and limited in scope (Agriculture) or Vast (Nature). More than one Divine Deity can exist and pull power from a single sphere of power (Life or War) may have multiple overlapping Deities attached to it.
Deities also exist outside the mortal realm on other planes of existence. The echo of their domains sustains them, but true power is drawing power from mortals who invoke their names. Mortals who pray to them, who give offerings to them, who perform deeds for their deities. Both good deeds and evil ones; are both powerful acts.
The passion of mortals is the ambrosia that deities seek. Therefore, beings of such immense power seem to care what happens in the mortal world. Why they help and hinder us. For our joy, sorrow, love, and hate; gives them the essence they truly seek, the power that fuels their divine energy.