I can’t load my images from a js file using wp_localize_script

You’re not accessing the value correctly. The 2nd argument of wp_localize_script is the name of a JavaScript object that your data will be added to. In your case it’s wpa_data. This means that the image_path is accessed at wpa_data.image_path:

$(function(){
    jQuery(document).ready(function() {
    $('#home').backstretch([
       wpa_data.image_path+"home-bg-slideshow1.jpg",
       wpa_data.image_path+"home-bg-slideshow2.jpg",
       wpa_data.image_path+"home-bg-slideshow3.jpg",
        ],  {duration: 2000, fade: 750});
    });
  })