"I feel as though my grandmother is guiding my hand" is far different than "I was my great, great uncle in a former lifetime" yet the latter is not that uncommon of a statement. The fact is that many modern Ásatrú folk have come to this reconstructed ancient religion by way of the neo-pagan scene in America (or elsewhere) and are having a difficult time accepting the fact that reincarnation is not part of the northern Germanic cosmology. Let's clear the matter here: reincarnation is not part of the northern Germanic cosmology! Now, if your panties are not in a complete, unknotable, wad, let's look at the matter a little more closely.
Question: Why isn't it? Isn't there enough evidence to show that reincarnation in fact exists?
Answer: Back up a minute. Reincarnation is part of a worldview. Many folks would love to think that reincarnation is a provable fact, but the data are clearly lacking. Let's just leave it as part of a worldview for a moment.
A general (very general) definition of a worldview is that it is a theory that allows participants to make certain predictions about their environment, at least in the near future, within an acceptable margin of accuracy. For people in Tibet or India, reincarnation explains, for example, how one member of a family can demonstrate mannerisms, problem solving strategies, and aesthetic choices as an ancestor that he or she has never met. Often, these individuals look like the forebear as well. Based on such observations these people can predict with a fair degree of accuracy the basic course of the child's life, and such predictions, after all, are important.
The eastern worldview then serves to explain such a particular transcultural phenomenon. The explanation without getting too technical or specific is that an individual travels through several incarnations for one reason or another. A soul is born and it begins its journey on a quest to perfect itself; once a level of perfection is achieved, the soul rejoins the One, from which it was originally born. Granted my explanation is overly simplistic, but it is functional.
We see the same phenomenon here in the West, and the current trend is to blindly jump onto the eastern mysticism bandwagon and attempt to show where reincarnation must play some kind of role in the eddaic or sagaic literature somehow neglecting that the explanation for what appears to be reincarnation. First of all most moderns do accept that genetics plays at least some kind of a role in how a person looks. (Some would like to believe that genetics is a good rationale for acting out their own xenophobic fantasies, but we are not discussing xenophobia, anti-semitism, or any other form of silly pseudo-science; just simple genetics like you learn in junior high school will do.) From a genetic point of view (which is, usually, acceptable to modern Ásatrú folk), children look like their parents because they've inherited that genetic material (kind of anti-mystical when you think about it). Reincarnation is not required here.
Our cosmology also says that luck is passed on through family lines. The amount of luck we have is based on who our family is and who we choose to associate with. If we marry and have children, the luck of both parents is intertwined to make up the luck (ON-hamingja) of the child. Parents with much luck have lucky children, and vice versa. Debts are also passed on in the same fashion; the Celts called this geis, but we don't have a word for it. Note: hamingja is not part of the so-called soul; it is how we access luck and often takes a female form. When we die it does not stay with us in the Land of the Ancestors, but moves on almost of its own accord. This is not reincarnation; we are not reborn in the next generation.
Sometimes, for us northerners of European descent, it appears as if the ghost of our ancestors are helping us out. This is the explanation for Christian and Heathen alike. The ghosts of our ancestors do help us out. Why? A variety of reasons usually only known to the ancestor who is doing the helping. Maybe he or she likes us, or looks upon us as one of their own children, or sees potential in us. This is part of our cosmology and has survived the onslaught of Christianity from Heathen times. It does not require reincarnation.
The Dalai Lama explains to us that he is the reincarnation of a long line of Dalai Lamas; from our point of view, however, he is an individual who has been chosen and nurtured by a long line of ghost-Dalai Lamas and who is carrying on that tradition. The Tibetan spiritual philosophy sees this as reincarnation; ours does not
Question: So why doesn't the Faith of the northern Germanic peoples accept reincarnation?
Answer: We don't really need it. It's unnecessary, and it clutters up our cosmology with a bunch of New Age crap.
Question: What about that line from the Second Lay of Helgi Hundingsbane?
Answer: What about it!? If that is the thing that you are going to base your entire argument on, completely ignoring the fact that it is a prose line obviously added into what was an older poem, and ignoring the fact that it is a literary twist which basically only appears one time in the Eddas, and ignoring the fact that there is no folk tradition of reincarnation coming out of northern Germanic Europe, then somewhere in a city near you there is probably a Magic Circle which has your name embossed in a No. 2 lead pencil on a piece of masking tape near the Western Watchtower! Reincarnation is part of somebody else's worldview.
Smart-assed question: How can you know? Maybe there was a secret cult of reincarnationists in Germanic northern Europe that you don't know anything about?!
Answer: I am a seiðman; I know. I've been in the Otherworld countless times, and I have yet to have anyone sidle up to me and say: "See that guy over there? Don't pick on him cause that is me reincarnated." Plenty of times I hear "Leave him alone 'cause he's mine to care for," but nothing about reincarnation. Sorry, Charlie.