The Deuspora live and travel in a mobile pocket dimension known as the Exilarchy. The Exilarchy is formed of the various Heavens, Hells, Underworlds and sundry other divine realms that belonged to the deities making up the Deuspora. As a result, it can be a very confusing place for those first coming to it. A valhallan feasting hall is just next door to a pagoda that was once used to house the souls of the damned. Golden fields suddenly becoming hellish canyons or roiling seas, without warning.
When the Deuspora land on a certain plane, parts of the Exilarchy manifest on the physical plane, usually in the form of buildings through which you enter the dimension itself. A sure sign that the Deuspora have settled are buildings that belong to no architectural style extant in this world, or that have not been extant for a long time.
Some of the Deuspora have been able to keep other paraphenalia of their godhood since their exile; these might be artifacts such as thunderbolts and aegises or entities such as dead souls, demonic guard dogs or many-legged steeds.
The current leader of the Deuspora is Harrumar, a True Neutral sky god who once was considered the most powerful of his pantheon. His world is gone, his followers killed by plague, leaving him no worshippers. His counsel has steered the Gods-In-Exile well these last few centuries, and have kept them from making too much trouble.