Difficult to give you an exact answer because I don’t know the PHP code you are using to print the menu. You will need to have a loop and insert a // between the <LI> elements, except for the very last one because you don’t want a // at the end of the menu.
For the CSS/HTML part you can follow chimpchomp’s lead and insert a span between each <li>, like this:
<li>HOME</li>
<span>//</span>
<li>HOME</li>
You will need to amend the margin betern each LI so that the // appears exactly centred between the menu options. You have this at the moment:
header nav ul li {
display: inline;
margin: 0 0 0 20px;
padding: 0;
}
You could change this so that the margin is the same for left and right, something like:
margin: 0 10px 0 10px;