No.

Although Halo was originally intended to be the engine for a new version of Myth, that idea was abandoned early in development.

Although Halo was originally intended to be a third-person game, like Oni, and there was some technology sharing between the two development teams, Halo does not use Oni's engine.

The upcoming game Myth 3, being developed by Mumbo Jumbo for Take Two Interactive, uses a Myth 2 engine modified to create a fully 3d game. That engine is in no way related to Halo or Oni.