As with all Wiedergangers, try to prevent getting surrounded so they cannot exploit Backstabber; good to have Underdog perk as a counter-measure.
They can only attack once per turn unless Possessed. The ones armed with two-handed weapons will not be able to move and attack, unless Possessed. Thus, if you push away a twohander fallen hero, he will not be able to attack on the following turn in the absence of a necromancer.
Their bite is fairly dangerous against unarmored brothers.
Good target for Nets, Stun and Disarm.
Flails' Lash skill is effective on ones with no head armor.
Use Throwing Spears and/or Axes to destroy shields, if ready to concentrate damage on ones equipped with particularly dangerous 1-handed weapons and/or to more consistently disable the Possessed ones.
Beheaded Fallen Hero with destroyed shield and/or lost weapon gains early turn order.
Use armor-destroying weapons like you would on Orc Warriors: Warhammers, Fighting Axes, Billhooks, Polehammers.
Reanimated Fallen Heroes with no armor left can be quickly dispatched by Decapitate skill.
You can pick up their weapon before they rise again (weapons have a chance to get destroyed if they rise or are reanimated).
Using daggers to puncture and loot their armor can be a great way to get durable (if fatigue inefficient) protection early on, especially since they can be armed with mid tier one handed weapons. Doing this if they come armed with two-handers is risky unless you have a good brother with Taunt to keep them occupied.
Raise Undead will raise any type of wiedergangers and skeletons (with 50% of their ) and any dead humans, can be used 2 times a turn, can't be used if someone is standing on the corpse (has unlimited range)
Use a brave (high ) team member perked with Rally the Troops (Sergeant) to avoid panic and fear
Use brave or perked (Fortified Mind) team members with high Melee Skill to engage in melee (better with easy to hit weapons like spears and swords)
Note: it is still possible (though increasingly unlikely) for morale to drop via Horrific Scream with resolve values of 95-119; but suddenly, when you reach a value of 120 resolve (i.e. 96 plus Fortified Mind, or 87 plus Fortified Mind plus the Sergeant's Sash), you become immune to Geists and they no longer even attempt to terrify you with Horrific Scream - they will engaged in melee with that brother(s) instead
By using the Adrenaline perk at opportune moments (i.e. when there's an opening and no danger of being surrounded by Fallen Heroes with Greataxes), spear-wielding brothers with relatively mediocre resolve and melee skill will have at least half a chance to kill a Geist before it gets another chance to do any spooking
Thorned and Battle Whips are capable of hitting at distance of 3 tiles and thus can dispatch Geists at their maximum attack range