Hi Welcome to Sitepoint 
You need to remove the nested lists from the flow so they don't impact on the layout. That means the nested uls should be position:absolute.
You don't need any of those classes as all items can be accessed from #nav quite easily.
e.g.
Code:
<!DOCTYPE html>
<html>
<head>
<link href='menustyle.css' rel='stylesheet' type='text/css'>
<style type="text/css">
body {
font-family: 'Lusitana', serif;
font-size: 14px;
margin: 0px;
padding: 0px;
color: #444;
background-color: #f6f6f6;
}
/* remove the list style */
#nav, #nav ul {
margin:0;
padding:0;
list-style:none;
}
#nav li {
float:left;
padding-left: 10px;
padding-right: 10px;
border: 1px solid #DDD;
text-transform:uppercase;
height:30px;
line-height:30px;
position:relative;
}
#nav li li {
text-transform:none;
float:none;
white-space:nowrap;/* or use a width*/
height:auto;
line-height:normal;
}
#nav ul {
position:absolute;
display:none;
top:30px;
left:0;
}
#nav ul ul {
left:100%;
top:-1px;
}
</style>
<link href='http://fonts.googleapis.com/css?family=Lusitana' rel='stylesheet' type='text/css'>
<script src="http://code.jquery.com/jquery-latest.min.js" type="text/javascript"></script>
<script>
$(document).ready(function() {
$('#nav li').hover(
function () {
//show its submenu
$('ul:first', this).slideDown(100);
},
function () {
//hide its submenu
$('ul:first', this).slideUp(100);
}
);
});
</script>
</head>
<body>
<ul id="nav">
<li><a href="#">Home</a></li>
<li><a href="#">Courses</a>
<ul>
<li><a href="#">Item 01</a>
<ul>
<li><a href="#">Sub Item 01</a></li>
<li><a href="#">Sub Item 02</a></li>
<li><a href="#">Sub Item 03</a></li>
</ul>
</li>
<li><a href="#">Item 02</a></li>
<li><a href="#">Item 03</a></li>
</ul>
</li>
<li><a href="#">Student Services</a>
<ul>
<li><a href="#">Item 04</a></li>
<li><a href="#">Item 05</a></li>
<li><a href="#">Item 06</a></li>
<li><a href="#">Item 07</a></li>
</ul>
</li>
<li><a href="#">Current Students</a></li>
<li><a href="#">Future Students</a></li>
<li><a href="#">Helpful Links</a></li>
</ul>
</body>
</html>
For accessibility the off-left method is better than display:none but won't work nicely with your slide down.
Also you should make the menu work without js to start with using :hover and then enhance it with JS afterwards. In that way you will still have a working menu when js is disabled.
e.g.
Code:
<!DOCTYPE html>
<html>
<head>
<link href='menustyle.css' rel='stylesheet' type='text/css'>
<style type="text/css">
body {
font-family: 'Lusitana', serif;
font-size: 14px;
margin: 0px;
padding: 0px;
color: #444;
background-color: #f6f6f6;
}
/* remove the list style */
#nav, #nav ul {
margin:0;
padding:0;
list-style:none;
}
#nav li {
float:left;
padding-left: 10px;
padding-right: 10px;
border: 1px solid #DDD;
text-transform:uppercase;
height:30px;
line-height:30px;
position:relative;
}
#nav li li {
text-transform:none;
float:none;
white-space:nowrap;/* or use a width*/
height:auto;
line-height:normal;
}
#nav ul {
position:absolute;
top:30px;
left:0;
}
#nav ul ul {
left:100%;
top:-1px;
}
.nav ul{display:none}
.nojs li:hover ul{display:block}
.nojs li:hover li ul{display:none}
.nojs li li:hover ul{display:block}
</style>
<link href='http://fonts.googleapis.com/css?family=Lusitana' rel='stylesheet' type='text/css'>
<script src="http://code.jquery.com/jquery-latest.min.js" type="text/javascript"></script>
<script>
$(document).ready(function() {
$('#nav').removeClass('nojs');
$('#nav li').hover(
function () {
//show its submenu
$('ul:first', this).slideDown(100);
},
function () {
//hide its submenu
$('ul:first', this).slideUp(100);
}
);
});
</script>
</head>
<body>
<ul id="nav" class="nav nojs">
<li><a href="#">Home</a></li>
<li><a href="#">Courses</a>
<ul>
<li><a href="#">Item 01</a>
<ul>
<li><a href="#">Sub Item 01</a></li>
<li><a href="#">Sub Item 02</a></li>
<li><a href="#">Sub Item 03</a></li>
</ul>
</li>
<li><a href="#">Item 02</a></li>
<li><a href="#">Item 03</a></li>
</ul>
</li>
<li><a href="#">Student Services</a>
<ul>
<li><a href="#">Item 04</a></li>
<li><a href="#">Item 05</a></li>
<li><a href="#">Item 06</a></li>
<li><a href="#">Item 07</a></li>
</ul>
</li>
<li><a href="#">Current Students</a></li>
<li><a href="#">Future Students</a></li>
<li><a href="#">Helpful Links</a></li>
</ul>
</body>
</html>
Hope that helps
You may be interested in superfish which works on the suckerfish menus and automates a lot of the js work.
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