Jump when he does the stomp and just evade the fireball. After a short time he will come after you. If you have any strong attacks, get ready. When he comes after you, you can usually get in a good shot or two. After hitting him, jump back quickly to avoid the punches or being grabbed. Try to stay close to the statues, but be careful. Shujinko's (Liu Kang's) Bicycle Kick works very well when he comes after you, and use sword attacks when he gets close. After awhile of playing, you can learn his patterns and better prepare yourself. The Dragon King's arena is bordered evenly by all six pieces of the Kamidougu.
The most effective way above all to defeat Onaga with any character is to back away from him, leaping over any ground attacks or projectiles he uses, then lure him towards the edge. Collecting a Kamidougu piece will stun Onaga for two seconds and even subtract from his health.
Take advantage of this opportunity by unleashing your character's longest and most damaging combo, then back away when finished. Repeat this process using another Kamidougu icon.