It is not known to evolve into or from any other Pokémon, despite its close resemblance to Hydreigon. However, despite not evolving from Hydreigon, Hydreigod is known to be the result of a fusion involving a "fallen" Hydreigon and Arceus.
No method exists to legitimately obtain Hydreigod in-game.
Hydreigod appears twice in-game. First it appears as a Pokémon used by Elite Four member Wilson as one of the so-called "Six Kings" of his team used in the Hall of Masters. Its second appearance occurs on Wilson's team in the Challenge Championship. Not much is known about Hydreigod aside from the fact that it was synthetically created, as described by Sir_Willis_CMS in the data given from the "Hall of Masters Laboratory Records":
Hydreigod, the primal terror. Dangerous creation caused by harnessing the primal power of Arceus and implanting it in the body of a fallen Hydreigon. Potential power level unknown. Kept in check with sealing mechanisms.
Because Hydreigod cannot be obtained by the player, it is not possible to obtain a full list of the moves it is capable of learning. However, there are a few moves that are known from the player's Sigil Hall and Challenge Championship battles with Wilson.