How to create simple tree menu using PHP or HTML but without JS?

Stu Nichols at CSS Play would be a good place to start looking at.

IMHO, it's bad form. But you could use the GET method with links to pass values to your PHP file then return the appropriate response to the page.

ie.

<?php
    if(!isset($_GET['link'])){
        $_GET['link'] = ""; // if not set, gets dummy value
    }

    $link = $_GET['link'];

    function showPage($link){
        switch($link){
            case "home":
                echo "<a href='page.php?link=homesub1'>Home Sub Menu 1</a><br>";
                echo "<a href='page.php?link=homesub2'>Home Sub Menu 2</a>";
                break;
            case "other":
                echo "<a href='page.php?link=osub1'>Other Page Sub Menu 1</a><br>";
                echo "<a href='page.php?link=osub2'>Other Page Sub Menu 2</a>";
                break;
        }
    }
?>
<a href="page.php?link=home">HOME</a>
<a href="page.php?link=other">Some Page</a>

<br>
<?php
    if($link != ""){
        showPage($link);
    }
?>

Obviously, a lot of thought has to be put in for the design to work. It's a disaster but it gets the job done.

Note: A better approach to this would be to convince whoever is in-charge to let you use JS/jQuery.