Eda is a fake, sunglasses wearing nun in the black market organization of Roanapur called the Church of Violence. She's a friend of Revy, but also a deep cover agent of the CIA on an unknown mission.
Eda is not her true name. She is an American citizen who is a member of the CIA in Langley, Virginia. On an unknown, deep cover mission she was sent to Roanapur as "Eda" from Alabama to take part in the black market gunrunners call the Church of Violence. This group is run by the elderly Yolanda but she is aware of her true identity. While there she has even made friends with the member of the Lagoon Company, Revy.
Her first appearance was in Black Lagoon Volume 2 CH. 9 "Calm Down, Two Men PT.1", and her first anime appearance was in Black Lagoon - Episode 7 "Calm Down, Two Men". Her character in the Japanese series is voiced by Jun Karasawa, and the U.S. dub produced by Ocean Group is done by Lisa Ann Beley.
Eda's character was rumored to have been modeled after Thana from the exploitation film "Ms. 45" (a.k.a. "Angel of Vengeance").
Eda is on relatively friendly terms with Revy and Rock from the Black Lagoon crew. She occasionally shares a bottle of booze with Revy, and yanks her chain on purpose by threatening to steal Rock away from her if she doesn't move on him first. None of the main cast seem to realize her real job with the CIA.
Eda usually keeps her history close to her chest, so not much is known about her origins. What is usually known is that Eda is posing as a nun at a Catholic Church, though she engages in very few nun-like duties. Instead, she helps her boss Yolanda sell and procure weaponry for any group with the right amount of cash. She also keeps a Glock 17L in a shoulder holster to settle any violent disputes.