Other than his part after Ragnarök, nothing is known about Móði. Magni is a part of the myth of Thor's battle with the giant Hrungnir.
Thor hit the giant in the head with his hammer, Mjolnir. Mjolnir broke Hrungnir's skull. The giant fell down dead with his leg on the neck of Thor. The other gods came to lift the leg off of Thor. They were not strong enough to lift it. Magni was only three days old. He came to his father and lifted the leg off of him by himself. Thor gave Magni the horse Gold-Mane. Hrungnir had owned the horse. Odin was upset that Thor gave the horse to "the son of a giantess" and not to Odin, Thor's own father.