First, the basics. There are nine Outer Planes, each attuned to one of the nine ethical/moral alignments. We are told explicitly that manes, lemures, and larvae are the souls of the chaotic evil, lawful evil, and neutral evil dead, respectively. These creatures are used as raw materials for the creation of devils, demons, etc. While there are no analogous creatures given for the good or neutral souls of the dead (based on Gygax's theory that the monster books should be filled with things for the player characters to overcome, and overcoming devas and the like wasn't consistent with the way he saw the game), Adventures Dark and Deep will have them; animae for the souls of the lawful good who go to the Seven Heavens, etc. Creatures with souls (humans, halflings, dwarves, gnomes, and half-elves) remain in their afterlife forever (well, as "forever" as anything gets in a game where monsters roam certain afterlives looking for victims to slay and devour), while those with spirits (elves, orcs, etc.) will be reincarnated after some indeterminate time in their afterlife.
So the Outer Planes are the afterlife, and at least some of the inhabitants thereof are the souls of formal mortals who journeyed to the appropriate plane after their death. However, there are some interesting anomalies with this interpretation.
Psychopomps are beings who guide souls from the mortal world to the afterlife. Sometimes they are themselves gods or goddesses, such as the Norse Odin, Greek Charon, Roman Mercurius, etc. or other beings such as the Valkyries, and various angels in Judaism and Christianity. In some cases they chose, and in all cases helped to transport, the souls of the dead to the afterlife, which was often a journey in and of itself.
The Monster Manual has at least one creature that functions as a psychopomp; the night hag. Interestingly, the night hag is said to only take those who are of the most selfish evil alignment; neutral evil. This is significant because it would make sense for the night hags, as enemies and haters of good, to seize the souls of good folk and bring them down to Hades to enslave them against their will. However, they don't seem to be able to do this. This speaks to the notion that the means of the death of the individual is unimportant to its final destination. What matters is their moral/ethical alignment.
The Deities & Demigods book provides, perhaps, the answer, where it says:
Although time is meaningless to the soul or spirit, the long journey to the proper plane can take 3-30 days of tie relative to those in the Prime Material Plane. ... The road through the Astral Plane to their destination is clearly marked for the dead, but it is not free of peril. Some monsters roam the ethereal and astral planes at will, which is why burial chambers often include weapons, treasure, and even bodyguards to protect the soul on its journey.
Given the fact that travelers in the Astral plane do not encounter the dead, it seems that these "roads of the dead", while they exist within it, are not normally accessible from it, except for certain monsters who are able to penetrate them and imperil their travelers. Could various psychopomps help guide the souls/spirits of the dead along these roads? It would seem at least possible, and the nature of these roads is left to be explored. Could they vary in nature according to the plane of destination? The specific religion of the spirit/soul? Are they in fact the same for all, but the perception of the journey along the road differs from individual to individual based on their preconceptions learned during their lifetime?
Could they possibly be the souls of persons who got lost upon the road? Rather than making the journey to their intended afterlife, perhaps those undead creatures with overt connections to the Negative Material Plane simply never made it to one of the Outer Planes, finding instead the negative plane, and thus being cursed to undead status thereby.
The status of the soul of the material undead is another matter. For ghouls, wights, and ghasts, it could be argued that they are simply animal-like, with their souls having departed their mortal remains, which are left as animate, but soul-less, husks. Zombies and skeletons are simple animated objects that happen to have dead bodies as their physical components. But what of vampires, wights, mummies, and the like? One interesting bit in the entry for the vampire in the Monster Manual states:
Like all undead, vampires exist in two planes at once - in this case the material and negative material.
Did it perhaps stumble on the road, rather than getting lost? Could they, perhaps, be the afore-mentioned monsters that can assail the unwary dead as they walk the well-marked path to the afterlife? Could be. Could be.