Omni-Gay

Omni-Gay is a sexuality in which consists of people who are attracted to all genders and/or sex but have a preference of the same gender and/or sex. 
but omni-gay is just one of many acronym, so it doesn't have to be just tied to gay; these people can identify as omni-lesbian, omni-gay, omni-bi, etc. anyone can identify as this term as its inclusive to just who you're attracted to.