Questions Gods of Sufficiently Advanced Aliens and What can gods be afraid of? together with Robert Merle's book Le propre de l'homme (I beg your pardon, I did not find English name) brought me to following question:
What is exclusive property of god?
Immortality: No. Their lives may be tied to worshippers or at least being of world where they live. Else they are probably only advanced aliens. And also, there are some nations that are not dying for age (but that can be killed like anybody else).
Wisdom: Probably no. There may be some nations that are very poor-minded (but still able to live) and in comparison with them they (gods) have great knowledge. And also there may be nations (mostly long-living or immortal by age) with great wisdom. Also, like below, gods from one story may be equal to humans from else story - in wisdom.
Power: No. It is sure that gods are very powerful, but also their power may be very limited - for example by amount of worshippers, or else rules. Or also, there may be some people that find (mostly accidentally) ways how to handle great powers (even capable to destroy whole world). It is very based on own story - god in one story may be very powerful, but in comparison with humans (or else lower creatures) may be very weak.
Language: No. There are many nations using many languages - and they don't understand each other. Also, even animals have own language - that we don't understand.
Feelings: No. As they created humans as image of ownself - and humans created some gods as their images, it is irelevant to count feelings as it. Gods may love or hate each other - or they hate or love mortals.
War: Probably no. At least, because I don't know any story where gods would fight against each other. Only people fight in the name of any gods against other.
(Species) self-destruction: No. Probably only people are capable to fight against else people to kill them - until (species) self-dustruction.
... It is all I found at this time that can be counted as property of god. What else property can be counted as property as god - is any one of them that would be count as exclusive property of god?