On the subject of the Einherjar, there's precious little about their powers. For what it's worth, the Paranet Papers' write-up, has:
Powers: None. Really—they gain nothing from
being brought back to this world, except the
chance to fight as a mortal again. They’re very
highly trained combatants, however, with literally
centuries of experience at killing lots of
things. They don’t seem restricted by ancient
practices and are just as good with machine guns
and Kevlar as with axe and mail.
Weaknesses: They’re mortal. It’s possible that
they recover from injury faster than normal
people do, as a result of Odin’s blessing, but
that’s speculative.
The only other real data point we have is how Murphy's sparring partner in Ghost Story doesn't seem at all put out by her breaking his hand, which to me could imply that he expects it to heal up, but it's not dispositive.