my husband and I have been unable to see this girl her whole life up until now (her mum wouldnt allow us to). but her mother and stepfather were having problems with her, so now sends her to live with us. i have 4 younger children and so havnt looked after a teenager before. My sd believes she knows everything and argues with anything we tell her. She is an EMO which is like goth, she listens to death metal, she has cut herself, and she has boyfriends and is not a virgin. We make rules for her, but she says she will sneak out and do what she wants. My husbands approach is to belittle her, and laugh her when shes disrepectful. I have tried being caring to her and listen to her, but she doesnt listen to me. I feel like sending her back, i feel like i cant help her

im scared she will influence my younger kids, what can i do
i dont know how to say this. but alot of what you described (with exception of cutting, EMO, goth and death metals, but even EMO, goth and well death metal is not that major i think) actually fell into the spectrum of "normal teen behaviour", i mean yes, they definitely fell towards negative side, but i dont think they are that abnormal.
that said, it does not mean that you dont need to set "reasonable" & "realistic" boundaries on behaviours like her attitude and sneaking around. it just means not to see her in too negative of a light. also bear in mind to not fall into the trap of setting boundaries alone. you are her step mom and your husband is her dad, she need to feel loved too.
but you are not alone in feeling frustrated in dealing with a teenage kid.
but you need to remember she is a teenage kid, it is normal for her not want to talk or have a tete a tete with her parents or stepparents, esp she does not know you. so i think you need to remember this is not personal and you can only to your best to listen and counsel her, if she is not receptive, then just leave it. You tried your best. But the best methods when it comes to dealing with teenagers is to let them know you are always there for them and then let them come to you.
also based on the fact that she is cutting and listen to death metals, it seems like she is in some kind of emotional pain right now and may be using all those as ways to cope. i think the best thing to deal with those issues is to consult a professional, christian would be best.
he and she should be able to guide you and your husband on this matter.
but i dont think your husband way of dealing with it is helpful.
yes, by all mean be firm/assertive, but not aggressibe/belittle or laugh at her. it will just make things worse for her.
lastly continue to pray for her. remember there is nothing impossible to God.