Read the bones is a pretty good common, so yes. Deicide will exile all of your Athreos cards if it hits one of them. Trawler will still do nothing about it because it only affects the graveyard. I also don't remember if there are any cards that throw -1/-1 counters on creatures in standard. If your friends are running standard, then the trawlers should be replaced with something else. Edit: Oh, and Gods Willing. Perfect common card to use too.
I edited my post a while ago. I double checked and realized, but when they're enchantments the -1/-1 counters won't kill them, only if they become a creature again. However like I said before, the gods wouldn't see the graveyard and thus the Trawlers wouldn't need to be there. Unless of course, counter spells are present. If they're exiled, they're not in the graveyard. Exiling the gods is the best course of action for his friends. I agree with you there, but I still don't think the Trawlers are useful. It is. However, as the saying goes: Easy to learn, hard to master.