We've seen Angel's internal organs (when Gwen shocks him to life briefly). His heart (and lungs!) is as much a dried-up walnut as always stated. In the same shot, his lungs can also be seen shriveled up, which means he wasn't lying when he said he couldn't give CPR, despite vampires being able to talk, etc... It's metaphysics through magical reanimation, not science. The human body is transformed into a parasitic demon host. There are a lot of human organs going unused by the demon that just shrivel up. Even blood flow appears to be mystical, as it bypasses the heart entirely and has no need for oxygenation. Blood is used both for metaphysical animation and as a direct food source. Vampires will often pretend to take on physical functions and human characteristics in order to better fit in, but this is purely a survival tactic to deceive during the hunt, rather than a true necessity.
There's actually a deleted scene from Eternity with Rebecca asking questions about how vampirism works and Angel is actually the one who gives the "metaphysics" explanation.
The demon appears to be a blank slate with no personality, memories or feelings of its own beyond its own survival needs, which is why there's so much variation between vampires. The soulless vampire always reveals itself to be ruled by its survival instincts and is only capable of adaption (such as in the case of a chip) as a survival mechanism, but that doesn't mean the human is somehow still present. A low I.Q. human will never be anything but low I.Q. as a vampire with little for it to work with, whereas a high I.Q. individual or one with particularly exploitable personality traits is going to make a much different sort of vampire. However, there is nothing of the human being left once it has died and the parasite has entered through the bloodstream, essentially being ready to be birthed as a brand new individual by the next night with a blood link to the rest of its line. The original pure blood demon essentially bred itself through parasitic reproduction.
The human soul is in fact the full human animus, not just a conscience. The Master even refers to vampire/demon souls using this definition of it as an animus. The demon is its own individual. If a vampire is ensouled, there are two beings sharing the body; one re-inhabiting its former corpse, but needing the demon and feed it to keep from turning to dust. There was a comic that basically considered this scenario of what would happen if the demon were to be expelled from an ensouled vampire. The most likely answer would be that, rather than turn an ensouled vampire human, it would more likely turn the body to dust if the demon were no longer keeping that body alive. The human within their old body is no longer the owner of their former body's physiology and needs, even if the human becomes dominant over the demon in regards to control.
