calling for javascript function in php form

You didn't quote your echo output:

echo requiredFields();;

It should be:

echo "requiredFields();";

Otherwise you're telling PHP to execute the requiredFields() function, which doesn't exist in PHP. Hence the error. Your intent here is to tell the JavaScript on the rendered page to execute the function. So as far as PHP is concerned you're just outputting a string to the page.

Note also that this is a syntax error:

echo "Email sent!";

What this will do is emit the following to the JavaScript in your <script> block:

Email sent!

Which, of course, isn't valid JavaScript. You probably meant to output that somewhere else in the page.

Edit: You also seem to have a significant logical error in your code. If you remove the unrelated lines, your structure is essentially this:

if ($action=="")    /* display the contact form */
{
?>
    <script type="text/javascript">
<?php
} else {
    echo "requiredFields();";
}
?>
</script>

So... You only open the <script> tag in the if block, but you use that tag in the else block. By definition both can't execute. Only one or the other. So you're going to have to restructure this a bit.

Maybe close the <script> tag in the if block too, and then open another one in the else block? Or have multiple if/else blocks for the HTML and for the JavaScript? There are a couple of different ways to structure this. But you should see what I'm talking about when you view the page source in your browser. You'll see that, in the event of the else block, you're never creating a <script type="text/javascript"> line and therefore aren't actually executing any JavaScript.

Though, thinking about this some more, it doesn't make sense at all to have the JavaScript start in the if block. Since only the else block uses it. You can't define the function in the if and then try to use it in the else because, again, by definition only one or the other would execute. Maybe just move all of the JavaScript to the else:

<?php
$action=$_REQUEST['action'];
if ($action=="")    /* display the contact form */
{
?>
  <form  action="" method="POST" enctype="multipart/form-data">
  <input type="hidden" name="action" value="submit">
  *Name:<br>
  <input name="name" type="text" value="" size="30"/><br><br>
  *Email:<br>
  <input name="email" type="text" value="" size="30"/><br><br>
  *Message:<br>
  <textarea name="message" rows="7" cols="30"></textarea><br>
  <input type="submit" value="Send email"/>
  </form>
<?php
}
else                /* send the submitted data */
{
?>
  <script type="text/javascript">
  function requiredFields() {
      alert("Please fill in all fields!");
  }
<?php
    $name=$_REQUEST['name'];
    $email=$_REQUEST['email'];
    $message=$_REQUEST['message'];
    if (($name=="")||($email=="")||($message==""))
    {
        echo "requiredFields();";
    }
    else
    {
        $from="From: $name<$email>\r\nReturn-path: $email";
        $subject="Message sent using your contact form";
        mail("[email protected]", $subject, $message, $from);
        echo "alert('Email sent!')";
    }
?>
</script>
<?php
}
?>

Honestly, this mix of PHP/HTML/JavaScript you have here is a little confusing. Which isn't making this any easier for you. You'll probably want to re-structure this a bit once you get it at least working.