Thanks for the feedback ya'll!
Under what classification do Denials belong to, or do they not belong to any specific classification?
Depends on the card. Reverse Time is definitely a Domin card, and Earthquake is definitely a Break card. Discord and Devourer are more complicated and probably require their own entire category (Devcord?). Devcord decks are bad against Rushes, which can get the quanta they need pretty quickly regardless of denial. Devcords are good against Breaks and Hybrids, which typically require more quanta to perform. Devcords are bad against Stalls due to Sanctuary, and they're a toss-up against Domins.
Are stall OTKs Hybrids or Breaks?
I'd consider them Hybrids, since I've defined Breaks to be almost entirely focused on offense.
Is there a general way of beating hybrids?
I think a large part of why Hybrids are so strong is because the cards they use are overpowered. Fractal nullifies an entire hand of the opponent's CC cards. Fire Bolt can be used either to kill most creatures in the game, or take out a quarter of your opponent's health in the late game. Dimensional Shield, Fahrenheit, Sundial, Psion, Phoenix...I could go on. If it wasn't for these cards, Hybrids wouldn't be as much of a problem. Winged Flying Titans, for instance, is one of the more balanced Hybrids. It's much slower than regular Flying Titans, and Wings is insufficient defense against many different decks.
Now, as for beating them, you should be pretty well off with a Break, because these decks can ignore the Hybrid's defenses and deal damage faster. If you want a Break that resists both CC and Shields, you have a handful of options: Flying Titans, Fractix or Fractal Psions, Shard of Freedom Mono, Pulvy Stone Dragons. Devtal is also a pretty safe bet, although it's not your typical Break. Unfortunately SoV, Poison, and Unstable Gas tend to be too slow for a pure Break deck. Also, you can oftentimes expand your options if you can rule out a certain type of deck (ie Dimensional Shield is banned, so you can use Flying Morning Star as a Break).
Is sundial balanced?
Nope! It's really not. I feel like when zanz made that card, he wasn't really expecting creatureless decks to be such a good strategy (remember, the old Sundial was even stronger), but this is just speculation.
Denial looks like a Hybrid deck. Some temporary defense plus bypass offense.
Eh, it doesn't really bypass that well, thanks to Sanctuary. I'm also not a fan of having very much temporary defense included in a Denial, but that would get explained in the quanta post.
Stall OTKs go into the stall category. They tend to have large amounts of defense and small amounts of bypass offense which are buffed by momentum to get around shields. Limitless speed is a good example.
This is really just semantics, but I personally count them as Hybrids because their defenses are not intended to last a full 23 turns, only long enough for an OTK.
Could there possibly be a "non-viable" deck that actually works? For that matter, would Stall OTKs be an acceptable category to go into the non-viable slot as they tend to have a different win condition than deckout?
Their offense is bypass, though. An OTK isn't stopped by CC or Shields. And their defense is temporary, moreso than permanent. A deck in the non-viable category would be able to win by deckout, but also by direct offense. It's too much to cram into a single deck.
Could you compile a short list of what the current meta-game decks fall into? I know some are Swallow, Pestal, Ghostmare, Wise Dragons, and Psiontal. You've mentioned a couple as Hybrids, so it'd be interesting to see where the more used decks end up.
From elk's list (plus a couple)
Disquake Bow - Devcord
Phoenixbolt Control - Hybrid
Light Firestall - Stall
THE DECK - Stall
Grabbow - Rush
Catatitans - Break
Adrenastaves - Domin
It's A Trap - Domin
Immorush - Rush
Ghostmare - Rush/Domin
Psiontal - Hybrid
FW Vamp Daggers Bow - Domin
Vader Saders - Domin
No Flaming - Domin
AM Monoentropy - Devcord/Domin
Pdialsbow - Domin/Hybrid
RT Shriekerquake - Domin/Break
Toadfish Bacteria - Rush/Domin
Dragonbow - Hybrid
Bonebolt - Hybrid
Adrenavamps - Domin
Devtal - Devcord
Pulvy Smash - Break
Mono Darkness - Devcord
I omitted the decks I wasn't familiar with. Some of the decks can be different types, depending on how they are built (more CC = Domin). Ive also included the Devcord category, which I explained earlier in the post.
Perhaps the "non-viable" category, if a decent deck was built for it, could beat Hybrids.
Its defenses would be useless against Bypass damage, and its offense would be shut out by the opponents' temporary defense.
What category does SoW Reflect fall into?
I'd consider it a Domin. It's intended to beat Rushes and loses to Stalls.