Wow! That is a really deep question, my friend. I'll give my two cents... which tie into my Earthly spiritual beliefs.
      One Universe. That is the basis of it. Whether this is the same universe or a parallel one, the rules of the game are the same. There is a spiritual realm which exists all around; the matter in which it is made is on a lower level than the current "physical" world, which allows it to occupy the same space. When, let's say, a Mudokon "dies," the spirit loses control of the body on the physical plane because it is no longer able to function. In other words, it's dead. Okay, so the bond between the astral "spirit" and physical body is severed. The body decays in it's natural physical environment, and the spirit is now in it's natural environment: the spiritual realm. (Think ghosts, people. I have firsthand experience with them) Now, the next thing that happens is that the (continuing from the above example) Mudokon spirit's now ended physical incarnation is reviewed and "judged." This Mudokon may be a young spirit with few life experiences, or an old "well-traveled" spirit with many life experiences. Respectively, the Mudokon's spirit learns what it can from it's life, and if more lessons are needed to be taught, he is reincarnated into a new body; in a new situation, place, group, tribe, or what have you. This Mudokon's spirit may have even evolved beyond what he can learn from living on the planet of Oddworld, and may even be placed on a different planet in a different situation and civilization... or even in a different universe. The spirit is reborn into a new situation, in which new lessons may be learned. This happens over and over again until the spirit learns all that it can. It is then that it becomes "fully evolved."
      So really, spirits are the same all over the universe, and in others. One is only put in the situation in which the appropriate lessons are waiting to be learned... for one's own personal growth. I'm really tying this both into Oddworld and this world; per my understanding of the spiritual world. So who knows, some humans out there may have been incarnated as a Mudokon in a past life! Heh!
      Oh yes, I forgot to mention... the birds in Abe's Oddysee and Exoddus simply portray a tangible means of Abe's spirit leaving his body.