answer; You'll find a variety of beliefs among Heathens.
Partial reincarnation - the fetch part of the soul returns to the family/adopted family line
the mound - a dreamless sleep unless disturbed (tales of that in the lore)
Asgard/Vanaheim - if one has earned a place among the elite, the soul goes to the hall of their patron deity.
Hella's realm - if one hasn't won a place in one of the halls, they move to a paradise-like afterlife in Hella's realm
Hella's Hall - those who were dishonorable in life - oath breakers, murderers, rapists, etc - go to the River of Knives or to Hella's Hall (it's not a nice place)
I believe that I will go to Valhalla if I die as a warrior. Otherwise I'll go to Heimdal's hall. I hope I am NOT reincarnated into my family because my family is fucked up. If I am reincarnated, I hope I will be born into a more loving and compassionate family.
Unless you're an abomination and end up actively cursed (you have to fuck up really bad to end up either chewed on by Hela's dogs, on the river of knives or in someplace like that), most people will spend some time as ancestor-spirits, at least until the last descendant they've personally known dies, then move on: either to a new birth, Hel in some cases (It can also be a place of rest, if not of bliss, for the non-cursed), or to a God's hall in the case of the worthy.
As far as I'm concerned, as long as I can fulfill my responsibilities as an ancestor-spirit, I don't really care if I'm reincarnated or forgotten in Hel, or whatever, although being invited to a God's hall would be a great honor.
Heathens today do not agree on the nature of the afterlife. That is to be expected, since the "Old-Time" Heathens didn't agree either. They simultaneously held numerous and perhaps contradictory opinions on the matter. A good place to start reading is H.R. Ellis Davidson's The Road to Hel; you can read it on line for free at one of the links below. The biggest bone of contention seems to be what, if any, forms of reincarnation/rebirth the Ancestors believed in. My own take is fairly nuanced in regard to this question. I think that "reincarnation" or "rebirth" include several phenomena, some involving the "recycling" of the person's essential "self," others involving recycling or linking to various parts thereof. Since most Heathens today believe in some form of multipartyTeoul, it's not an either/or thing. Also, I think that various cultures at various times picked up on one or more of these phenomena. In any case, Heathenism in all its manifestations stresses this life without ignoring or denying the afterlife. We don't tremble in fear of a final judgement nor do we deny ourselves life's pleasures in the present in hope of some reward beyond the grave.