Omni (or omnisexual) means that a person can feel attraction to people of all genders, and that gender is perceived or has relevance in that attraction (unlike pansexuality, where it is usually not). It does not imply equal attraction to everyone, but rather openness to all genders.
Gaybian is a hybrid term used for people whose orientation moves between gay and lesbian, or who don’t fully fit into just one of those categories. It can include experiences such as: feeling gay in one way and lesbian in another, having a complex gender identity (butch, transmasc, non-binary, etc.) that allows “gay” and “lesbian” to coexist, loving from a place that is not strictly heterosexual and doesn’t fit binary labels
So, being omni-gaybian can mean that:
the person can be attracted to people of all genders (omni), but lives that attraction within a gay/lesbian framework, not a heterosexual one, and their way of loving and desiring is shaped by a specific queer identity (for example, butch, transmasc, non-binary, etc.).
In simple terms: an omni-gaybian is someone who can love people of any gender, but whose orientation and way of relating are still gay/lesbian, not straight, and not reducible to a single label.