I cleaned up the code a bit and added comments to indicate more clearly where changes need to be made if you want to use this override:
/* EDIT -- latest code  (more cleanup) */
<?php
// No Direct Access
defined( '_JEXEC' ) or die;
?>
<?php
/*identify the search for which this is an override  ***CHANGE TO MATCH YOUR SEACH LIST NAME */
   $searchlistname = "search_by_features";
/*
identify the field names for the checkbox fields and the text we want to use as header text. ***CHANGE THESE TWO LINES TO MATCH YOUR FIELD NAMES AND the TEXT you want to use as Headers for each of the fields 
*/
   $myfeaturesarray = array("veh_features","veh_navigation_features","veh_audio_features","veh_features__exterior"); 
   $myfeaturesnames = array ("Interior ","Exterior","Audio/Media","Navigation");  
   
/*
set up class styling in your custom css for  these two classes Example:
.sebcboxclass {
     width:200px;
     float:left;
     border:1px solid #eee;
   }
   .sebcboxlabelclass {
     display:inline;
   }
*/
/*
the contentof the submit button was extracted from the source of the page before overriding 
*/
     $submitbutton = '<div id="cck1r_button_search"><div id="cck1r_form_button_search"><button type="button" id="button_search" name="button_search" onclick="JCck.Core.submit('."'save'".');return false;"><span></span>Search</button></div></div>';
   
   $arraycount =  count($myfeaturesarray);
/* 
move through each of our checkbox fields
*/
   $x=0;
    do {  
     $myid = $myfeaturesarray[$x];
     $thename = $myfeaturesnames[$x];
     // get the checkbox values as string of options with || separator then explode it into an array
     $myveh_features = $cck->get($myid)->options;
     $valuearray = explode("||",$myveh_features);
     $vcount=0;
     echo '<h3 style="clear;both">'.$thename . '</h3>';
/* Now that we have the options in an array, we will run through them to show the input checkbox and its label.  For styling, we enclose those two tags inside a div. */
     foreach ($valuearray as $value) {
       $string1='<div><input id="' .$myid . $vcount .'" type="checkbox" size="1" value="'.$value.'" name="'.$myid.'[]">';
       $string2 = '<label for ="'.$myid . $vcount . '">'.$value .'</label></div>';
       $vcount++;
       echo $string1.$string2;
     }
     $x++;
     echo '<div style="clear:both"> </div>';
   }while ($x<$arraycount);
/*Now show the submit button. */
   echo '<div>';
   echo $submitbutton;  //show the submit button
   echo '</div>';
   ?>