The keys open one of four chests. If it is the first time you have used a key from a Wormfeeder rune you will get a calcified fragment, after that they just give you engrams/materials/CoO runes.

Blind Thralls. If you follow invisible platforms to the far back left of the mausoleum area, there's a platform with a chest that says "smell is the key" also there are three invincible "blind thralls" that spawn when you land on this platform. Go back to the main part of the mausoleum, and on the right wall (right side if you're facing the open pit, left side if you're coming from the blind thrall platform), just before the door to the court of oryx area, there's a small cave with worms on the ground. Wait there for a minute and you get a buff called "stench" or something. Get back to the blind thralls quickly and they won't attack you while you have this buff. You will also be able to open the chest.

Poison Chest. There are praying acolytes who periodically spawn in the three areas near the Court of Oryx. Killing them will sometimes cause Taken to spawn. Killing those taken will sometimes cause a relic to spawn (you'll get a message saying the relic was summoned from the void). Pick that relic up and carry it to the stench room and you and your fireteam will be immune to the stench damage, allowing you to safely open that chest. Apparently you can also cheese open the chest using a titan bubble.

Sometimes you get a chest key from the court of oryx bosses.

Skybreaker's Chest. There's a series of dropped items from the skybreakers. First item is a random drop off of any skybreaker (I got mine during the "two brothers" strike). Use it in a terminal near the Dreadnaught Patrol spawn (run towards the mausoleum, it's in a small hole in the side of the ship just before you leave the zone) to summon a skybreaker champion. Kill that guy to get the next key. Use that in a ship console accessed via the ship entrance near the mausoleum (I believe?), kill that guy to get a console key. That key is used in a special room to open a door and the chest. Here's the location of the special room: From the entrance to the mausoleum, if you run left to the skybreaker's ship, you'll run directly beneath the special room. You can climb a broken part of the dreadnaught to jump into the room.

Argonach's Chest. This rune drops randomly from Taken champions on ship. You have to charge it by killing taken champions. There are 7 total whom you have to kill. When you finally do that, you can use it on a console in the are where the wardens are, just outside of the Asylum. That console summons more taken to kill, and killing them all spawns the chest.

Chest of Gnashing Teeth. Located under the portal in the Court of Oryx. First you need a wormsinger rune (random drop from hive and taken). Put that in a console near where dreadnaught patrol starts to summon a hive champion. Kill that guy to get a wormfeeder rune. Kill 50 enemies on the dreadnaught without dying and you'll get a key from it. 1/4 is the Key of Gnashing Teeth. I forget which ones are the other 3 keys.

I have a theory that the key you get is dependant on the final enemy you kill. I know I've had Key of the Spawn both times I've ended on a Major Centurion, and have another person who got one from either a Centurion or Wizard (it was a grenade kill so he couldn't be certain which kill counted).

If anyone could test it and let me know that'd be awesome.