Similar to what Crab said, the gods are conscious minds from particular concepts manifested through Chaos itself.
"There is no way to know the true face of a Chaos God, for no mortal or machine mind can grasp the unfathomable nature of Chaos. The Four Powers are manifestations of the various aspects of this pure Chaos, and thus they, too, can only be described in limited mortal terms, using words and images that must ultimately fail to perfectly represent the god's actual form."
In this case it could be said that their manifestations are similar to demons but more OP, for example, Skarbrand producing a "crack" in Khorne's armor, this clearly indicates a "physical" manifestation in terms of warp.
Some reasoning regarding chaos indicates similar things, although it usually varies.
"Other commentators have suggested that Tzeentch, the Great Mutator, has no fixed shape at all. Tzeentch's tangible form, when he chooses to manifest physically, is a mass of constantly shifting flesh. Thus, the constantly fluctuating material body of the Changer of Ways resembles many of his creations, such as his daemons and his realm itself, which similarly have no stable form. Still others have posited that Tzeentch's physical forms are simply images that mortal minds create to try to perceive and understand something far more abstract, an agent of pure change, mutation, and flux."
This manifestation is sustained by the craziest use that can be given to the concepts that they embody.
For example, Khorne and the conflict:
"All across the universe, in every galaxy, on every planet, and in every passing moment of time, conflict has steered the course of events. It is conflict that has propelled one species into a position of dominance over another and consigned one man to oblivion while another has triumphed. There are as many sources of conflict as there are beings in the universe. Jealousy, rage, sport, hunger, political advantage, territory, possessions, or even the simple, innate thirst for domination all breed and foster conflict. It is inescapable. There has never been a time or a place free from it. Even those races claiming to be enlightened and peaceful cannot escape the basic truth that without conflict, their progress would come to a halt, with challenging new ideas being left unconsidered...Khorne is conflict embodied to its most violent extreme, and thus Khorne is eternal and omnipresent. In all places and throughout every era, Khorne's influence has been felt by all."
"The fundamental conflicts that drive mortal life forward sustain Khorne on a base level, much as bread and water might sustain a creature of flesh. But just as a mortal body craves more substantial food, so too does Khorne desire greater conflicts. He is not content to lurk in the background, inciting petty squabbles or drinking in the joys of a remote border dispute. Khorne is not some mere beast or other lowly temporal being. He is a god, and the appetite of a god is terrible and insatiable...Above all, Khorne seeks the spilling of blood. Through murder, slaughter, and war, servants of the Blood God rip apart the flesh of their enemies, staining the soil on thousands of worlds with crimson gore, all in the name of Khorne. Nothing pleases Khorne more than the free flow of sanguine life force. It gives him his power, sustains him, and eases the spreading of his influence"
Slaanesh and the pleasure:
"these are just a few of the countless facets that make up Slaanesh, because while its core stems from the experience of pleasure, Slaanesh can also be seen as an amalgamation of all the various impulses and emotions that surround the experience and concept of pleasure. These impulses and emotions can include, for example, joy, satisfaction, aestheticism, romance and love, and the potentially most dangerous feelings of greed, selfishness, lust, lust and perversion. However, they are all linked, and dangerous feelings often develop from the most innocent."
Some stories indicate similar things.
"In the beginning there was the void, and only the void, and the gods moved across the face of the void and they were made wholly of it. Some will tell you that a void is a nullity, a nothingness. They are fools. The void is everything; its infinitude encompasses all possibilities and their ultimate annihilation. It pleased the gods to shape the void as they passed through it, giving it form at their fancy for a time before their makings collapsed back into primordial sea. When the gods met they battled and coupled in equal measure, their shapeless offspring sleeting into the void to lie forgotten in the shadows. So it was for an eternity, with only the void lit by the fire and lightning of the gods at sport."
