As you say, the most well know aspect of the Heathen conception of the afterlife is Valhalla, [The Hall of the Slain] where the Valkyries take those slain warriors whom they have chosen for Odin.
These warriors, the Einherjar, spend their days fighting to the death all day then every evening coming back to life to feast and drink till morning till the time comes to fight their last great battle at Ragnarok, the end of the world.
Odin however, ever the pragmatist will willing accept those who die outside battle if they are courageous and noble of spirit.
Odin does not have it all his own way, for half those slain in battle belong to Freyja.
They dwell in Her Hall, Sessrumnir [Many Seats], and as she is the Goddess of fertility perhaps their lives there are altogether more delightful then the shenanigans going on over in Valhalla.
However it appears that Freyja would also welcome those who died outside battle, as indicated by the case of a woman, Thorgerda,in Egil's saga. She threatens to commit suicide after her brother's death, saying: "I shall not eat until I sup with Freyja". So she expected, even though she was not a warrior, to dwell thereafter in Freyja's hall.
Those not chosen by Odin or Freyja live in Hel, which was simply the dwelling place of the dead. It was
not a place of punishment; in fact, gold and mead are in plentiful supply.
Some of the dead are believed to reside in spirit in their Howe or burial mound and there are stories of the living attempting to communicate with their dead forefathers by sitting out on the family howe.
I do not think it is a matter of belief on the part of the dying Warrior or Shield Maiden The truth is that s/he is needed to fight the last great battle against those who would destroy the universe. Until that time comes s/he is taken care of by Odin or if one of the lucky ones by Freya
Fortified Midgard, lies encircles by the ravening Worm.
Over its icy bastions faces of giant and troll
Look in, ready to invade it. The Wolf, admittedly, is bound;
But the bond will break, the Beast run free. The weary gods,
Scarred with old wounds, the one-eyed Odin,
Tyr who has lost a hand,
Will limp to their stations for the last defence. Make it your hope
To be counted worthy on that day to stand beside them;(C.S Lewis)
dav