Deoxys is waiting for you every day on Birth Island in one of his 4 forms and is ready for a fight! To get to Birth Island you need the Aurora Ticket. You can buy it for 50,000 Pokédollars or get it daily as a reward from the Sevii Island Bounty Challenge.
The Hoenn Trio is waiting for you in the Embedded Tower near Route 47. You need the move Rock Climb to get there. With a Jade Orb you can awaken Rayquaza, Kyogre and Groudon. You will then have to fight an epic battle against them.