Tom - I've seen so many problems caused by with views on views on views in the past that I've denounced them as heretical and will never write them myself. You definitely have your work cut out for you. You're going to have to examine the performance of each view and underlying table. You're going to have to look at every UDF and figure out what they do and how. Performance improvement opportunities will present themselves.

I'm offering this piece of advice because it sounds like a real mess, I don't know what environments they have for you to play around with and you're new to your job. I don't do any changes like this on the production database until it's thoroughly tested for both results and performance. I would follow the same advice here. I don't want your first month at your new job to be your last because you brought down a production server.