The Omniverse is the massive sphere or bubble that makes up all of existence, including most -verses, realms, dimensions, concepts, etc, except the Godverse(s) and Beyond Realm. Only a select few structures that exceed this space are classified as existing.
The Omniverse holds all of reality. Containing everything imaginable (or at least connected to).
An alternate definition of the Omniverse is that it contains an infinite number of these "layers"; universes combine to make multiverses, multiverses combine to make megaverses... and the stack, which can be called an infinite fractal array of archverses, keeps going forever. In this way the Omniverse could be a direction one approaches rather than a physical set containing some infinite number of -verses.
Not many entities or civilizations can achieve or even fathom exiting the Omniverse, either being denied access to the exterior by Creator or Destroyer, or simply not being advanced enough to jump through an infinite amount of spaces. However, it has been done by many highly advanced civilizations, and even some small teams, such as Satoru's crew.
The only trait every single thing within the Omniverse share is that it exists. How it exists varies in countless ways.
Beyond the Omniverse
The Omniverse exists in the surrounding emptiness known as The Outside, a void of virtual nothingness. Whatever may lie outside of these concepts is simply referred to as Beyond, one of the many iterations contained by Transcendentem.
Two Godverses orbit the Omniverse, one belonging to Creator, and one to Destroyer.