Applying for more than one faculty position in a department
You imply this is a US institution you are concerned with. While only they can answer the question directly, and you should ask them, I think an application that covers all of the positions, would likely be acceptable. 

I've assumed this is for a single department, of course, which likely has a single hiring committee. If they are hiring for three closely related positions then I'd think that they could decide which is a better match for yourself and themselves. 

I would simply state my qualifications in an application, emphasizing elements that would be suitable for each of the positions. If you are interesting enough to them that they want to actually follow up and talk to you then you can refine things a bit, but I wouldn't try to guide it too much in the application. 

In fact, I think a lot of places would find it odd to get three applications from the same person for a position in one academic department. That is so unless, for example, they indicate that there are actually three committees with three different chairs. In that case, you could send identical applications to the three chairs, mentioning that you have sent identical requests to the others.