In the world of ghouls, they are not harmed by normal metal, they need to be harmed by the kagune, their natural weapon built from their RC cells. That world also has no adamantium, so in this scenario we shall make this metal harmful to ghouls.
Wolverine family I think of are; Logan, Daken, X-23/Laura Kinny, and the addition of Old Man Logan. They all have their speed, fully functioning fast responding healing factor, and sense of smell.
A kick to the nuts won't make a Wolverine momentarily down for the count temporarily.
For those who don't know; the Aogiri Tree are a militia of sinister ghouls, so they are very well trained and powerful, but unlike Wolverine and Deadpool, decapitation is fatal to ghouls even with their natural healing ability.
Devising a strategy for this scenario is up to your imagination, you can let them go in with a strategy, or attack in haste in the reckless Wolverine fashion who has 200+ years of combat experience and martial arts education.