I took some time today and tested out all of the attack types that you have noted in your post as potential problems. I was able to confirm that all of these sources of damage were triggering at least one type of eater.
Bleed damage and armor ignore damage were triggering the all damage eater property as these two sources of damage are considered direct damage. Word of death was triggering various eaters as it was inflicting chaos damage.
When I started casting strangle on myself I thought you may have found an issue, however once I started casting it on one character using a second character I was able to confirm that it was indeed triggering both the poison and the all damage eater properties.
If you find any other sources of damage that you think may be broken with regards to the eater properties, please feel free to let me know.
