Well, I'm sure Magister will be in here shortly to fill you in on all the details, but I'll give it a shot.
Each god has a seperate vault (heaven/hell) which is an reflective of their sphere that they are. For example, if you look in Sphener's pedia entry, it shows that Junil's vault is very ordery with almost everything having a law that govern's it. When Bhall fell, she actually left her original domain (one of holy fire) and crashed into Agares' vault, Nyx. around the area where she landed you get the classic hell look of fire and brimstone but in the rest of Agares' vault it's a more dark and gloomy place. It is worth noting that Agares originally had a very beautiful vault before he fell and was still the god of hope, but destroyed it all after his fall to spite the One. As for the relationship with humanity, they can only act through their followers, so the gods with a religion in game are some of the most active, but others include Ceridwin, Mammon (through Hastur, his archangel and the OO) and the rest of the evil gods, who are tend to be more manipulative than the good gods. and of course Danalin is asleep so he has no concious relationship with his followers.
As for their relation with eachother, they tend to get along well with the other gods whose spheres match theirs, while they don't get along very well with gods whose sphere's are opposite of thiers. For instance, Mulcarn and Bhall are still huge enemies despite the fact that they are both evil. Sirona, the godess of spirit, is tended to be treated like a little sister by the other good gods due to her (excessive) compassion for others. She is the only (?) god who believes that Agares can be redeemed.
Each gods power in Creation is dependent on how stong and faithful his followers are. The compact dissalows the use of direct divine interference by the gods but the more that a group of people in Erebus are loyal to the god (knowingly or unknowingly) the more the gods can act. For instance, Agares can't put a Balor in the middle of Torrolerial but if Bannor armies and marching into Sheiam lands, if people call for his aid, he can slip in a few demons. Technically, the stronger demons shouldn't ever be allowed out of hell terrain due without breaking the Compact but that's not in the game to make it more fun.
Basically, for the evil side, where the corruption spreads, demons can go.