The second batch of Starters you will find are the Pokémon whom trainers start with when they begin the journey in Kanto. In Heart Gold & Soul Silver, these Pokémon are obtained by visiting Professor Oak after you have obtained all 16 Badges and defeating Red.
Kyogre & Groudon are both available within this game. To access them, you need to obtain the Blue Orb if in Heart Gold or the Red Orb if in Soul Silver. These orbs are found from Mr. Pokémon after you have obtained the National Dex and received the Kanto starters from Professor Oak.
In order to get the Kanto starters and the Red/Blue Orb, you need to get all 16 Gym Badges and defeat Red.
Sources: This and this.