For now, think in terms of drastically condensing your background, referring to publications by a summary number, rather than by citations, and stressing your transferable skills. An exception is firms that do highly technical work in your field of graduate study. For some of those, a document which looks very similar to a C.V. is appropriate. If you're fortunate enough to get an interview, don't even think about trying to wing your way through a case question. You'll be competing with people who've been practicing for months.
Several books are available to help.
Also check out consulting companies' Web sites. Some include material on case interviews, and sometimes offer interactive cases. In this regard, the Boston Consulting Group's Web site is particularly helpful. If you can, find someone to practice with. You'll both benefit.