As a user, filling multiple contact forms is really annoying, irrespective of the UI. Why not restructure the entire contact form as a single page. There is a reason why every registration form is a single-page process, which is to ensure that the process of asking data from the user does not irritate him.
Use the conventional 'required field (*)' concept, but focus on an attractive, but clean UI. The user will go through the form, and fill only what is necessary, and may even fill more if the UI is neat and clean.
I would never recommend a multiple-page contact form. You could bring in some user interactive features, like button, radio boxes and drop downs, but make sure you don't try and extract too much data from the user, just for the sake of asking them details.
Collect only the details you actually need, say Name, Email, Number and provide only a couple of 'not mandatory' fields for the user. The user will know automatically that he need not fill in those details. You need not tell him that he has the option to skip certain fields, because it will be obvious to them, provided you take the 'required field' concept.
As far as UX is concerned, the lesser content, the merrier the page.