Here I am covering only the characters featured in the OAV. There are many more in the manga but I am not familiar with them. Besides, I'm only covering the Angel Sanctuary OAV here.

From Earth

Setsuna Mudo

Setsuna is a high school student who unknowingly is a reincarnated angel. Setsuna is constantly getting into fights with people and doesn't have many friends. He is also in love with his biological sister Sara. Setsuna lives with his father (since his parents are divorced) because his mother hates him and thinks the devil is protecting him. Setsuna will do anything for Sara and only gets to see her when they're away from home. He tries to protect her from his own sinful feelings, but eventually the truth comes out and he and Sara run away together. Setsuna is conflicted in that he doesn't want to accept that he is actually an angel and only wants to be together and happy with Sara by his side.

Sara Mudo

Sara is Setsuna's younger sister. She misses being with Setsuna so she arrages times for them to meet throughout the week. She hates to see Setsuna get into trouble and gets angry when he gets into fights. She has strong feelings for her brother and even falls in love with him. She gives up everything to run away with Setsuna because she can't stand to be apart from him. She devotes herself to protecting him and pays dearly for it.

Mrs. Mudo

Setsuna's mother. She takes care of Sara and can't stand Setsuna. When she catches him and Sara together she tells him off and sends him away. Fearing for her daughter's safety and soul, she tries to send her to an all girls school in England.

Kato Yue

Kato is a classmate of Setsuna's. He's a creep that beats up Setsuna and sometimes hangs around with Kira. He does a lot of drugs and gets himself into trouble by buying some off of Rociel. The drugs manipulate him into attacking Setsuna, where he dies in battle against Alexiel.

Kira Sakuya

Sakuya only appears in spirit, and is actually the original inhabitent of Kira's current body. Sakuya died as a child in a car accident. Before the spirit (who we now know as Kira) who took over Sakuya's body did so, he asked what Sakuya wanted. Sakuya never wanted his father to miss him when he was gone, so he requested that the spirit make his father hate him.

Mr. Sakuya

Sakuya/Kira's father. He worries for Kira and remembers the days when he was a good child (which was before the real Sakuya died in the accident). Mr. Sakuya dies in the destruction Setsuna causes.

From Heaven

Alexiel

Alexiel is the angel that rebeled against God by joining with demons from Hell and because of that was sealed away into a crystal. Her punishment was to be reborn as a human for all eternity, doomed to suffer in life and die tragic deaths.

Rociel

Rociel is Alexiel's obsessive and mad twin brother. He is only focused on recovering Alexiel and ignores all of his duties in Heaven until he can get her back. He demands complete loyalty from his followers and is often cruel in his treatment of others.

Katan

Katan is like Rociel's servent. He comes to earth to beg Rociel to come back to Heaven to help out with matters there instead of obsessing about recovering his sister Alexiel. Katan soon realizes that Setsuna Mudo is Alexiel's reincarnated spirit and thus decides he must eliminate Setsuna in order to get Rociel back.

Adam Kadamon

One of the most powerful angels in Heaven. He watches over Setsuna and often helps him.

Metatron

We only get a glimpse of Metatron in the anime. He plays a role in the manga series.

Sevotharte

Like Metatron, we only see Sevotharte for a couple seconds at the end of the anime series. Sevotharte is a major character in the manga series.

From Hell

Kira Sakuya

Kira is Setsuna's close friend. He seems to be respected among other students and sticks up for Setsuna. He doesn't like to admit it, but he cares deeply for Setsuna and comforts him when he's in trouble. Kira's true origins are a mystery; his current body is one he asked to use from a dying Kira Sakuya. So he is actually the second spirit to inhabit Kira Sakuya's body. Kira is immortal as long as he has the blood spatter of Rociel imprinted on him from long ago.

Kurai

Kurai is a demon from hell. She looks much like a boy, but she is in fact a girl. She chases after Setsuna trying to awaken Alexiel. When heaven and hell were at war, Alexiel saved Kurai from being killed by angels. Ever since then Kurai has been in love with Alexiel and wants her back. Kurai soon takes a liking to Setsuna also, and begins to sympathize with his dilemma.

Arachne

Arachne is a Kurai's cousin from hell. Arachne is really a male, but he likes to wear women's clothing. He doesn't care so much about Alexiel, he just tags along with Kurai to keep her safe.

Prophet Dragons

Three wise spirits (the lead of which is Jade) who Kurai goes to for wisdom and advice.