The magazine was founded by Keeton and her future husband Bob Guccione, publisher of Penthouse Magazine. The idea for Omni came from Keeton who wanted a magazine "that explored all realms of science and the paranormal, that delved into all corners of the unknown and projected some of those discoveries into fiction."
The name of the magazine originally was Nova, but the name was changed to Omni to avoid any conflict with the PBS TV show.
SF authors published in Omni included Orson Scott Card, William Gibson, George R. R. Martin, Robert Silverberg, Norman Spinrad, Theodore Sturgeon, Thomas Disch, and Stephen King. Mainstream authors also contributed science fiction and fantasy stories. Fiction editors included Ben Bova, Robert Sheckley, and Ellen Datlow.
An annual The Best of Omni Science Fiction was issued in the early 1980s. After Volume 1 in 1980, new stories were also included.
There were other spinoffs from the magazine, including a television program and comic books.
For more on the magazine, see http://www.sf-encyclopedia.com/entry/omni