Before I go on, I'd like to say that without a Cheating Device, you cannot get these Pokemon from HeartGold.
Deoxys - Migrate from the GameBoy Pokemon Cartridges to Pokemon Pearl or Diamond by using the Pal Park. Afterwards, trade Deoxys to HeartGold or SoulSilver. (By the way, Deoxys can be found at Birth Island in the GameBoy Pokemon Cartridges.)
Mew - It seems that Emerald is the only GameBoy Pokemon Cartridge that has Mew. Migrate Mew to Pokemon Pearl or Diamond, like Deoxys, and trade it to HeartGold or SoulSilver. (Mew can be found at Faraway Island in Emerald.)
Celebi - Migrate from the GameBoy Pokemon Cartridges to Pokemon Pearl or Diamond by the Pal Park. Do the same with the others and trade Celebi to HeartGold or SoulSilver. (Nintendo Event is needed for this lovely Legendary.)
Chat with our AI personalities
Celebi
you find out in the celebi event, but it deals with Giovanni.
To get celebi, there is an event that has only been realeased in japan
this is it: 52247d8c 582000c0 12247d8a 00004801 02247d8c e0021c39 02247d90 000000fb d2000000 00000000
you use it to put in the shrine to cath celebi