<?php
global $post;

//checks to see if the terms exist inside the cpt's
$termnews = term_exists('homeone', 'news');
$termtestimonial = term_exists('homeone', 'testimonial');
$termcasestudy = term_exists('homeone', 'casestudy');

//checks the amount of posts in each term
$posts_in_news = $termnews->count;
$posts_in_testimonial = $termtestimonial->count;
$posts_in_casestudy = $termcasestudy->count;
//conditionals to check if the term is true
if ( $termnews == true && $posts_in_news >= 1 ) {
//output the loop in here
}

if ($termnews == true && $posts_in_testimonial >= 1 ) {
//output the loop in here
}

if ($termnews == true && $posts_in_casestudy >= 1) {
 //output the loop in here
}

?>