comments_popup_link() – how to load different classes/images according to different comment condition?

Use get_comments_number() to determine the number of comments, and prepare the CSS class with that information:

$css_class="zero-comments";
$number    = (int) get_comments_number( get_the_ID() );

if ( 1 === $number )
    $css_class="one-comment";
elseif ( 1 < $number )
    $css_class="multiple-comments";

comments_popup_link( 
    __( 'Post a Comment', 'your-theme' ), 
    __( '1 Comment', 'your-theme' ), 
    __( '% Comments', 'your-theme' ),
    $css_class 
);