What are the prerequisites to encounter the legendaries in ORAS?

Here's the prerequisites for each legendary encounter. If you accidentally defeat them and save, you may need to rebattle the Elite Four for them to reappear.

Having since tested this again, note that any prerequisite Pokemon don't necessarily need to be caught in 6th generation games as was previously stated.

Tornadus/Thundurus/Landorus

• Available on: Omega Ruby (Tornadus), Alpha Sapphire (Thundurus), Both (Landorus)
• Location: Sky above Fortree City (Eon-Flute, Black Storm Cloud)
• Required Party Pokemon:
  • Tornadus/Thundurus: Castform
  • Landorus: Both Tornadus and Thundurus
• Required Item: None
• Date/Time available: Always available

Terrakion/Virizion/Cobalion

• Available on: Both Omega Ruby and Alpha Sapphire
• Location: Pathless Plain (Eon-Flute, Red Spark Near Pacifidlog Town)
• Required Party Pokemon: 3 Pokémon fully EV-Trained (Obtained once a Pokémon's stats cannot be raised anymore.)
• Required Item: None
• Date/Time available:
  • Terrakion - Tuesday/Saturday
  • Virizion - Monday/Thursday
  • Cobalion - Sunday, Wednesday and Friday

Mesprit/Uxie/Azelf

• Available on: Both Omega Ruby and Alpha Sapphire
• Location: Nameless Cavern (Eon-Flute, Red Spark near Sootopolis City)
• Required Party Pokemon: 3 Pokemon with Max Friendship/Happiness
• Date/Time available: (Exact times are still being properly tested)
  • Uxie - between 20:00 and 21:00
  • Azelf - between 21:00 and 03:59 and
  • Mesprit - between 04:00 and 19:59.

Dialga/Palkia/Giratina

• Available on: Omega Ruby (Palkia), Alpha Sapphire (Dialga), Both (Giratina)
• Location: Sky above Dewford Town (Eon-Flute, Tear in Sky)
• Required Party Pokemon:
  • For Dialga/Palkia: Azelf, Mesprit and Uxie
  • For Giratina: Palkia and Dialga
• Required Item: None
• Date/Time available: Always available

Lugia/Ho-oh

• Available on: Omega Ruby (Ho-oh), Alpha Sapphire (Lugia)
• Location: Sea Mauville (Surf and Dive required)
  • Ho-oh will be on the deck
  • Lugia will be in the basement
• Required Party Pokemon: None
• Required Item: Tidal Bell - Which is a reward for returning the Scanner from Sea Mauville to Capt. Stern. Find the scanner in the (otherwise pretty empty) basement, trade it for the Tidal Bell, and return to Sea Mauville.
• Date/Time available: Always available

Raikou/Entei/Suicune

• Available on: Both Omega Ruby and Alpha Sapphire
• Location: Trackless Forest (Eon-Flute, Red Spark near Rustboro City)
• Required Party Pokemon: Ho-oh or Lugia
• Required Item: None
• Date/Time available: Every 20 minutes
  • Raikou: Visit between xx:00 – xx:20 (e.g. 1:01 – 1:20)
  • Entei: Visit between xx:21 – xx:40 (e.g. 1:21 – 1:40
  • Suicune: Visit between xx:41 – xx:00 (e.g. 1:41 – 2:00)

Zekrom/Reshiram/Kyurem

• Available on: Omega Ruby (Reshiram), Alpha Sapphire (Zekrom), Both (Kyurem)
• Location:
  • Reshiram/Zekrom: Fabled Island (Eon-Flute, Red Spark near Mauville City)
  • Kyurem: Gnarled Den (Eon-Flute, Red Spark near Mt Chimney)
• Required Party Pokemon:
  • Reshiram/Zekrom: 1 Pokemon at level 100
  • Kyurem: Both Reshiram and Zekrom
• Required Item: None
• Date/Time available: Always available

Heatran

• Available on: Both Omega Ruby and Alpha Sapphire
• Location: Scorched Slab (Cave on Route 120)
• Required Party Pokemon: Pokémon with Surf and Strength known
• Required Item: None
• Date/Time available: Always available

Latios/Latias (Post Game)

• Available on: Omega Ruby (Latias), Alpha Sapphire (Latios)
• Location: Southern Island (Requires Eon Ticket, talk to Dad at Petalburg Gym first and follow the story from there)
• Required Party Pokemon: None
• Required Item: Eon Ticket
• Date/Time available: Always available after receiving Eon Ticket

Cresselia

• Available on: Both Omega Ruby and Alpha Sapphire
• Location: Cresent Isle (Random Mirage Island off the coast near Ever Grande City)
• Required Party Pokemon: None
• Required Item: None
• Date/Time available: Randomly (and rarely) appears when updating Mirage Spots (go online to 'pass-by' trainers and increase your chances of it appearing)

Regice/Registeel/Regirock

These Pokemon need to be unlocked before they can be encountered:

Unlocking:

1. You need to put Relicanth at the front of your party, and Wailord in the 6th position. Note it has to be Wailord, not Wailmer.
2. Fly to Pacifidlog Town, and head West to the fast currents.
3. Stick as south as possible on the fast currents until the island with the trainers. Then, stick to the middle.
4. You should end up in a place where you can Dive, surrounded by strong currents.
5. Dive down and head south as far as you can go
6. Read the Braille text, and resurface.
7. Head up and again, Read the Braille text, and use Dig.
8. Enter the tunnel and read the next set of text. It tells you to put Relicanth and Wailord into 1st and 6th position respectively.
9. Do so and interact with the text again. This will set off 3 Earthquakes and unlock the Regi caves in the overworld.
10. Exit the cave, you no longer need any Party restrictions and can box Relicanth and Wailord.

Watch this guide for visual instructions

Once unlocked

• Available on: Both Omega Ruby and Alpha Sapphire, once 'unlocked'
• Location:
  • Regice: Island Cave, (a small reef on the west part Route 105). Wait inside for 2 minutes after reading the text. The door will open in 2 minutes.
  • Registeel: Ancient Tomb (Route 120). Use Fly in the middle of the room.
  • Regirock: Desert Tomb, (bottom of the desert in Route 111). The message reads: Go right twice, down twice and then use Strength and the door to Regirock should appear.
• Required Party Pokemon:
  • For Regice: a Pokemon with Surf
  • For Registeel: a Pokemon with Fly
  • For Regirock: a Pokemon with Strength
• Required Item: None
• Date/Time available: Always available after unlocking

Regigigas

• Available on: Both Omega Ruby and Alpha Sapphire, once 'unlocked'
• Location: Island Cave (same as Regice)
• Required Party Pokemon: Regice with a nickname (yes, really), Registeel and Regirock. Registeel and Regirock MUST NOT be nicknamed, and the OT for each likely has to be the trainer on the current save.
• Required Item: Regice needs to hold a frozen item (Snowball, Nevermelt Ice, CasteliaCone)
• Date/Time available: During the Day

References

• NintendoNewsFix
• Serebii
• PokemonDB
• Kotaku
• Personal Experience