Load page template with custom content using a plugin

You can achieve that with filters on the_content and the_title:

function wpa_content_filter( $content ) {
    if( isset( $_REQUEST['var1'] ) && $_REQUEST['var1'] == "str1" ) {
        return 'This content will be displayed on the default page template.';
    }
    return $content;
}
add_filter( 'the_content', 'wpa_content_filter', 999 );