Cuts:
-1 Nevinyrral's Disk -- too slow
-1 Icy Manipulator -- flexible, but too expensive. Straight up removal is better. Consider Vindicate.
-1 Batterskull -- This simply doesn't fit what the deck is trying to do. If you need a beater with lifegain, there are better options that fit angel/demon/dragon. If you really want to play this card, then also play Stoneforge Mystic and at least 1 other equipment.
-1 Tragic Slip -- Cheap, but there is more flexible removal that can fit this slot. Dismember might be a good option. -x/-x effects also hit indestructible.
-1 Exalted Angel -- This sucks
-1 Oblivion Ring -- Flexible, but it has a significant downside (can come back, and is sorcery speed). Maybe Mortify to replace.
Sign in Blood can be replaced by Night's Whisper -- Much easier to cast (or run both). Also consider Tormentic Voice and Faithless Looting
-1 Doom Blade -- Check out some of the other suggested removal below. Cut / Ribbons is much better. Creature removal with a wincon built in.
-1 Disenchant -- Check out some other suggested artifact / enchantment removal. Maybe Aura of Silence. I also think Fragmentize is often overlooked. Shattering Spree is also great if you just want artifacts.
-1 Lotus Bloom -- Awesome turn 1 & 2, but progressively loses value, and worthless by mid/late game. Replace with other artifact mana ramp.
-1 Shattered Angel -- Another beater is probably better. And there are better ways of gaining life.
-1 Elesh Norn, Grand Cenobite -- Awesome card, but you can't cheat it out. Unless your opponents are playing lots of small tokens, it might not even be high impact.
Adds:
+1 Rakdos the Defiler -- This is way better than first glance reveals. Putting it into combat using Kaalia allows you to skip the first effect. This forces a player to sacrifice half their permanents without the downside to yourself. Extra fun if you can give him double strike with Boros Charm.
+1 Lightning Greaves -- Kaalia is extremely weak to spot removal and this list currently doesn't run enough protection, and haste is a huge bonus with Kaalia. If you need more, you can also add Swiftfoot Boots
+1 Talisman of Indulgence; +1 Rakdos Signet; +1 Boros Signet; +1 Talisman of Conviction; +1 Talisman of Hierarchy; +1 Orzhov Signet; +1 Fellwar Stone; -- Pick at least a few of these. With the addition of artifact mana, you can probably drop some lands too (down to 34).
+1 Demonic Tutor -- I know you have one, and its obviously fantastic
+1 Doom Whisperer -- Stack the deck with Surveil. Helps keep the pressure on or find answers. Usually worth a few life.
+1 Rakdos, Lord of Riots -- Add this back to the deck. It is one of the stronger creatures in the deck.
+1 Archfiend of Despair -- EACH endstep! This guy is awesome!
+1 Crackling Doom -- Multiple removal at instant speed, and hits big voltron creatures that typically have hexproof! (Zur the Enchanter, Uril the Miststalker, Omnath, etc.)
Not Sure About:
Mana Vault -- This deck can't abuse it for ramp beyond its initial tap for mana. Might be better to replace with colored mana ramp.
Grim Monolith -- This deck can't abuse it for ramp beyond its initial tap for mana. Might be better to replace with colored mana ramp.
Condemn -- Path to Exile might be better (condemn requires attacking) - Or maybe use both.
Pyroclasm / Day of Judgment / Wrath of God -- All hit Kaalia and the rest of your board. Maybe pick 1 of these + Catastrophe. Merciless Eviction, Blasphemous Act, or Austere Command are other really good options.
Other Considerations:
Leyline of the Void -- Shuts down many decks, but anti-combo with any graveyard recursion you might play. Also see Bojuka Bog
Possibility Storm -- Might be insanely good in Kaalia. You don't necessarily need to 'cast' anything other than Kaalia. This is probably a game winner most times that you can resolve it.
Kolaghan's Command -- awesome and would be a good replacement for several cards identified above as being weak, but is surprisingly pricey ($20+)
Wheel of Fate or Reforge the Soul -- Wheel effects are really strong in Kaalia to load your hand with threats. Might be worth adding another alongside the existing Wheel of Fortune.
Balefire Dragon -- might be a one-sided board wipe
Skyline Despot -- Monarch is pretty solid if you can hang onto it. Gives card advantage and dragons!
Tariel, Reckoner of Souls -- Super fun and pretty strong. Can attack and use its ability because of vigilance (except the turn it is cheated in from Kaalia).
Yosei, the Morning Star -- Basically steals a turn from someone. Can really disrupt a single opponent for a turn when it dies. Good if you can guarantee its death with something like Sneak Attack. Can be a lock engine if you can recur this from graveyard each turn with something like Reya Dawnbringer.
Blinding Angel -- Weak body, but strong effect if you can land it against an aggressive deck.
Dragon Mage -- Wheel effect built into a creature. Wheel effects are strong in Kaalia, but it occurs post-combat, meaning you won't be able to sneak any more goodies in with Kaalia that turn.
Lathliss, Dragon Queen -- There are enough dragons that this might be strong.
Reya Dawnbringer -- Very high mana cost, but very strong if you can keep it alive for a few turns
Drakuseth, Maw of Flames -- Built in removal, but doesn't trigger on the turn its played using Kaalia.
Sire Of Insanity -- Super strong if you're ahead or combined with some graveyard recursion like Reya Dawnbringer.
Oreskos Explorer -- Might be cool as a one time Land Tax if you're behind on land. I've just never seen this card before, so wanted to throw it somewhere.
Sorin Markov -- Might let you one-shot people with his -3 ability the turn its played, or can use as removal. Pretty strong all around.
Liliana Vess -- This card is greedy and might not be great, but the -2 ability is crazy if you can manage to survive 2+ turns with it, or are comfortable enough to try climbing for the -8.
Darksteel Mutation -- It is pretty hilarious to cast this on someone's commander. This is some of white's strongest creature removal. The indestructible won't bother you because all your stuff has flying.
Chrome Mox -- great, but about $45 unless you wanna grab gold border ($12)
Winter Orb; Armageddon; Catastrophe. -- Land denial is very strong in this deck after casting Kaalia. You can cheat in threats, opponents can't. The effectiveness of this strategy increases dramatically as the number of artifact mana sources increases. I would remove an existing board wipe for Catastrophe at least.
Gamble -- Tutors are good, but this obviously comes with a downside.
Red Elemental Blast and Pyroblast -- Typically instant additions to a deck playing red, but our meta isn't super blue heavy. Up to you. I'd use at least one of the above.
Stranglehold is incredible at higher levels of play, but might be less effective in our meta.
Sneak Attack -- This deck might have enough threats to include this, especially with new additions. If you add this (you should) play more graveyard recursion or reanimator effects.
Phyrexian Reclamation -- Reload hand. Especially if you add strategies like Sneak Attack
Razaketh, the Foulblooded -- Pretty damn strong as long as you have some stuff to sacrifice. You can do this at instant speed in response to removal.
Mother of Runes or Giver of Runes -- More protection is good, can also be used to punch through opponents defenses.
Effects like Rule of Law, Ethersword Canonist, and Eidolon of Rhetoric hurt other decks way more than Kaalia.
Bogardan Hellkite -- Fatty with built in removal
Savage Beating -- can be a surprise win, especially with entwine
Angel of Despair -- Flexible removal on an angel body, this is quite strong
Aven Mindcensor -- This thing is brutal. Though might not be as good in our meta.
Iroas, God of Victory *list* -- Gives evasiveness, protects your creatures in combat, and can become a strong creature. Lot to love here.
Karmic Guide -- Returns something good to battlefield. Don't need to pay echo cost.
Linvala, Keeper of Silence -- Super strong denial.
Lyra Dawnbringer -- Very good depending on how many angels you run. Beefs them up, and gain some life.
Smothering Tithe -- Extremely strong mid-game mana ramp
Anguished Unmaking -- Another flexible removal at instant speed.
Lands:
Landbase needs a heavy rework. With proper artifact mana, you can cut down to around 34 lands comfortably. The landbase is frequently setting you behind a turn. Some tapped lands are okay, but make them count (e.g. tri-lands, scry lands, bounce lands, etc.).
Try only playing 1 cycle land. Cut either Barren Moor or Drifting Meadow.
City of Traitors is strong, but the downside is brutal. If you keep this in, I wouldn't count it as part of the 34 lands.
List of tapped lands: Barren Moor, Bloodfell Caves, Boros Garrison, Drifting Meadow, Evolving Wilds, Rakdos Carnarium, Rakdos Guildgate, Scoured Barrens, Terramorphic Expanse, and the Panoramas are colorless unless you pay + still enters tapped.
Good adds under $15 each include:
Temple of Triumph
Sacred Foundry
Clifftop Retreat
Battlefield Forge
Sunbaked Canyon
Rugged Prairie
Temple of Silence
Godless Shrine
Isolated Chapel
Caves of Koilos
Silent Clearing
Fetid Heath
Tainted Field
Temple of Malice
Sulfurous Springs
Graven Cairns
Molten Slagheap - storage lands are weird, but might be decent.
Luxury Suite
Shadowblood Ridge
City of Brass
Nomad Outpost
Path of Ancestry -- I've never seen this and its really good!
Urborg, Tomb of Yawgmoth -- I have one for you and is a definite add
Utility Lands:
Rogue's Passage -- Colorless, but unblockable is hot in this deck
Shizo, Death's Storehouse -- Again, unblockable
Vault of the Archangel -- Deathtouch + Lifelink
Eiganjo Castle -- Allows Kaalia to dodge pyroclasm and similar
Bojuka Bog -- Graveyard removal