The key is parrying.
The dungeon in the zone, which is situated in the southwest part of the map, has a clue. It says this: "I touched him once, but not again. I batted his staff away as he put it in my face. That's when I gave him a touch. The elderly untouchable
The trick is to block the Aged Ones, who are untouchable creatures, just before they swing their cane at you. They will rush you and try to swing their cane once they notice you. Say your prayers if you don't parry it and are unable to harm them. The only is this. When these foes are susceptible, you can't be worried if your parrying isn't up to standard. The easiest way to get past them is via stealth.
The Abyssal Woods are home to a variety of paths, many of which are completely devoid of Aged Ones. There aren't many necessary stealth moments where you'll need to be very cunning, but if you're impatient like me, it could be worth searching around for other options.
It's kind of hilarious that even while the game repeatedly informs you that there isn't a method to harm an adversary, there is still a way around it if you work hard enough. I suppose some fragile, maddening elders shouldn't be able to stop us if we're out here slaughtering gods.