We have hosted exchange students in the past and personally believe that sometimes students who should not be placed in the program due to lack of emotional maturity nonetheless are placed. What you are describing indicates, based on my experience, someone who has minimal English skills and who is struggling to be accepted because their language skills are not sufficient?
There are a range of options available to you. First option is to stick out until the 90 days are up. 90 days may seem like a long-time but it is not like you have her for a year.
Another option would be to speak with a teacher or your school counselor. They might be able to intervene for you with your parents. Reason why I suggest this is because the issue here I feel is that this student is not a good choice for your family because of the issues that it is creating and I feel maybe enough planning did not go into bringing an exchange student into your family. Though your posting presents only one side of the issue it does suggestion that communication has broken down and it needs to be restored between your parents and yourself on this issue. It is my feeling since this is causing you some distress that something needs to be done to work through the issue so that a satisfactory resolution is found. Hopefully by bringing in a third-party your parents and you can communicate effectively about the issue.
Third option will be to try talking to your parents again and present evidence to back up what you are saying. This means talking about being locked out of your room, and her sexual activity instead of focusing on emotive issues like her morality. At least from my experience making value judgments do not convince people they only entrench their position which prevents a solution being found.
Fourth option would be to speak to her directly about the issues in an assertive and constructive way. By this I mean not talking about value judgments. Instead talk about her behavior and how it impacts you. Hopefully this will relive some of the issues that exist.
Finally, you speak about contacting the program. At least from my experience dealing with exchange programs unless the student does something against the rules that puts their visa at jeopardy, such as being arrested, or they develop mental health issues that invokes their duty of care to the student then there is very little they will do. I suspect if you contact them the most they will do is talk to your parents and maybe try to resolve the issue. Personally, based on the information you have posted, my own feeling it is unlikely that they would remove her from the house based on your call alone and it would have to be your parents requesting it. However if it gets to be an untenable situation I would recommend using it as your last resort after trying different ways to resolve it.