With XPath you can fetch '<style>...</style>' and '<style type="text/css">...</style>':

$oDomInput = new DOMDocument();

$oDomInput->loadHTML($sHtml);

$oDOMXPath = new DOMXPath($oDomInput);

$oDOMNodeList = $oDOMXPath->evaluate('//style');

$oDomOutput = new DOMDocument();

if ($oDOMNodeList->length > 0) {
    for ($i = 0; $i < $oDOMNodeList->length; $i++) {
        $oDomOutput->appendChild($oDomOutput->importNode($oDOMNodeList->item($i), true));
    }
}

var_dump($oDomOutput->saveHTML());

However, this does not include style tags inside coditional comments '<!--[if gte IE 9]> ... <style> ... </style> <![endif]-->'.

With XPath you can fetch comments, conditional comments but also unwanted HTML comments:

$oDomInput = new DOMDocument();

$oDomInput->loadHTML($sHtml);

$oDOMXPath = new DOMXPath($oDomInput);

$oDOMNodeList = $oDOMXPath->evaluate('//comment()');

$oDomOutput = new DOMDocument();

if ($oDOMNodeList->length > 0) {
    for ($i = 0; $i < $oDOMNodeList->length; $i++) {
        $oDomOutput->appendChild($oDomOutput->importNode($oDOMNodeList->item($i), true));
    }
}

var_dump($oDomOutput->saveHTML());

In order to remove HTML comments from the HTML string use this Regex:

$sHtml = preg_replace('/<!--(?!\s*(?:\[if [^\]]+]|<!|>))(?:(?!-->).)*-->/', '', $sHtml);