Сделать порядок поиска PHP-глобуса нечувствительным

Для этого я бы использовал регулярное выражение. См. Последний блок кода для гораздо менее понятной, но простой версии.

<?php
//Its bad practice to use $_REQUEST, you should use $_GET or $_POST if you can..
$keywords = $_REQUEST['keywords'];

//Let's prepare our regex to match our keywords.   
$exploded_keywords = explode(" ", $keywords );
$regex = "/";

//Loop trough your keywords and add them to the regex.
// ?= is a lookahead, if you want to know what it does. http://www.rexegg.com/regex-lookarounds.html
//preg_quote() will escape your keywords so they don't break your regex. Caracters such as ( ) . ? * etc.
foreach($exploded_keywords as $keyword){
    $regex .= "(?=.*".preg_quote($keyword, '/').")";
}

/* 
 * The following block of code has been added just in case it's useful to someone.
 * This will return a match if ANY one keyword is found within the file name. (Case insensitive)
 *
 * $regex = "/.*(";
 * $tmp = '';
 * foreach($exploded_keywords as $keyword) {
 *  $tmp = $tmp."|".preg_quote($keyword, '/');
 * }
 * $regex .= ltrim($tmp, '|') . ").*\.jpg/i";
 */
//match a jpg file. This version is case insensitive for the keywords and the extension.
$regex . = ".*\.jpg/i";
//This would make it case sensitive but for the extension
//$regex . = ".*\.[jJ][pP][gG]/";

//Now let's get the files
$files = glob("*.[jJ][pP][gG]", GLOB_BRACE);

//Let's get our matches
//preg_grep will look in your array values for matches and return the entries as a array. 
//array_values will reindex the keys of the returned array. Otherwise they keep their original keys. 
$matches = array_values(preg_grep($regex, $files));
//Verify your results
print_r($matches);

Укороченная версия:

<?php
$keywords = preg_quote($_REQUEST['keywords']);
$regex = (!empty($keywords)) ? "/(?=.*". str_replace(' ', ')(?=.*', $keywords).")"  . ".*\.[jJ][pP][gG]/" : '/.*/';
$files = glob("*.[jJ][pP][gG]", GLOB_BRACE);
$matches = array_values(preg_grep($regex, $files));
print_r($matches);

Обновлено: добавлен preg_quote () при создании регулярного выражения, поскольку ключевые слова явно поступают из пользовательского ввода.