A lot of abilities work only on mortals, but there is no set definition for this in the class and it's not really specifically defined in general D&D terms. Would you say that, for the purposes of the God class's abilities, 'Mortal' refers to any living, corporeal creature with a maximum age? Even that is sort of vague, since a lot of monsters are mortal but have no listed maximum age.
I assume that certain creature types would be excluded, such as Undead and Constructs, since they are not alive and thus not mortal (for instance, upon being knocked down to 0 hp, they are specifically destroyed rather than killed). Many Outsiders are immortal, but not all of them are by my understanding. The creature type traits do not list being destroyed or any mention of being immortal (and the same goes for elementals) other than that both do not have a 'dual nature' (body and soul).
Also, are there any limits on what Portfolio the God can have access to? Most published deities have at least three or four items as part of their portfolio, but the number varies and doesn't seem related to degree of deity or anything else. Is this merely between the player and DM to decide on?