OK... this may or may not be as scientific a study as ones funded by the big corporations, but here's what I just did:
I took a cup of dry DE and put it on an aluminum pie pan. Another cup of wet DE (water soaking it through but no puddles on top) in another pie pan. A third cup of wet DE with bigger pieces of grit, small pea gravel, leaves, sticks, chicken feed, table scraps mixed in.
I dug in the garden and woods and underneath some logs and got a bunch of earthworms, garbage beetles, slugs, and assorted creepy crawlies. Didn't look for lice, fleas or mites, sorry.
Put about an equal number of each kind of insect & worm in each pie pan.
1. Dry DE killed anything soft skinned and really slowed down the hard shelled insects. The soft skins were torn open and the worm and slug guts were oozing everywhere.
2. Wet DE killed the soft skin critters but didn't slow down the hard shelled ones which just crawled out.
3. Wet DE mixed with stuff killed the soft skin critters, but it took longer because they tried to escape on the other stuff in the DE. Hard shelled critters crawled away.
Not gonna make any conclusions.