running a script in a php module

No there isn't, HTML doesn't support logic.

If all you need to do is selectively display an image, you should use PHP.

Code:

<?php
switch (1) {
    case 1: $img = 'Logo - Research Study Toolkit(3).jpg'; break;
    case 2: $img = 'Logo - Original2.jpg'; break;
    // case 3 + 4 omitted for brevity
    default: $img = 'Logo - Research Study Toolkit(3).jpg';
}

$src = base_url("assets/themes/default/images/{$img}");
$img = "<img src='{$src}' style='float:left;margin-top:5px;z-index:5' alt='Logo'>";
echo $img;
?>

(Also, creating a switch() on the value of "1" will always result in the same image appearing)