Yes -- a strong narrative voice would really help -- it must be authoritative and all-knowing (thus the term omniscient). It helps if the voice is unique and easily relatable.
Most omniscient narrators are unnamed, but it's also possible to have a narrator who is, say, a descendent of the characters in the story and he/she is recounting what happened.
Omniscient narrator does NOT assume the POV of the characters, unlike 1st or 3rd person limited. The omniscient narrator has its own point of view -- the all-knowing "guy." It does not filter anything through the characters. It may choose to report on what one character experiences, but it is still told from the omniscient narrator's POV.
Omniscient narrator can report anything it wants, but it should also maintain focus for clarity's sake. If it's reporting on character A, it's good to maintain that focus instead of jumping around. However, the narrator is allowed to report anything it wants ("Little did John know, the volcano was about to erupt.")
Omniscient narrator can have a personality. Imagine Zeus telling a story, and Zeus has a personality. He also might has his biases and philosophies, and he may "intrude" (narrative intrusion), but it's better to keep it at minimum.
Omniscient narrator should be reliable. Since the narrator is usually not part of the story, and it's all-knowing, and it reports on the whole thing, the readers come to trust the narrator to tell the truth. Unlike 1st person narrator, who can be unreliable or semi-reliable, the omniscient narrator should not lie to the readers, and it should not be "unsure" about anything. It is, after all, omniscient.