Use conditionals with wp_enqueue_style to attach stylesheet according to post type displayed

The issue in your first block of code is syntax:

if( get_post_type() == ( 'activity' OR 'dining' OR 'heritage' OR 'hiking' OR 'nightlife' ) ) :

this isn’t proper use of OR and will evaluate true regardless of what get_post_type() returns.

The issue in your second block is again syntax, you have to break; at the end of every switch case or the other statements after it get executed.