Installing multiple themes would become highly involved if you want each page to have a different theme. You could always build a different template for each page and have the page templates call specific CSS, header, footer, and sidebar files. This would be somewhat advanced and require a lot of coding.
Another option would be to use WordPress MU. This is a multi-user installation of WP that gives you essentially several different blogs (one for each of your podcast shows, for example). With this setup, it would be fairly easy to give each show it's own theme, as each would really be it's own site (usbn.net/rock and usbn.net/country, for example).
WordPress MU runs on just one database, so you don't need to set up separate installations at all. Just follow the directions at http://mu.wordpress.org/.