Stop header code from showing in category page?

You can achieve that by changing the conditional to

if ( !is_home() && !is_archive() )

Also consider using if and else if. So your optimized code would be:

<?php

    if ( !is_home() && !is_archive() ) {

        if ( get_post_type() == 'pretty-little-liars' ) {
            echo '<div id="headerimg"><img  src="http://tv-cafe.com/wp-content/uploads/2013/01/pllbanner.png"></div>';
        } else if ( get_post_type() == 'revenge' ) {
            echo '<div id="headerimg"><img  src="http://tv-cafe.com/wp-content/uploads/2012/08/revenge.png"></div>';
        } else if ( get_post_type() == 'grimm' ) {
            echo '<div id="headerimg"><img src="http://tv-cafe.com/wp-content/uploads/2013/01/girmmbanner.png"></div>';
        }

    }

?>