pcormack

Grand. We will leave the topic as theme related (css based) and resolve this.

Instead of display:none maybe use display:inline;?
The display:none is obviously not showing the links.

ul.twFeed li a:link, ul.twFeed ul li a:visited, ul.twFeed ul li a:active
{
display: inline;
color: #8c8c8c;
padding: 3px;
background-image: none;
}

My previous version was missing two lines which correctly formatted the widget. The problem is 100% the fact that links in your sidebar are styled to display in a block at 100% width.

This looks to be your themes CSS.
The sidebar links in unordered lists look for a block structure:

.sidebar-box ul li a:link, .sidebar-box ul li a:visited, .sidebar-box ul li a:active
{
display: block;
color: #8c8c8c;
width: 100%;
padding-top: 3px;
padding-right: 3px;
padding-bottom: 3px;
padding-left: 3px;
background-image: none;
}

This is causing the expected behaviour in your theme. You need to try to remove/change the width:100%; and display:block; lines. You can try by adding this to the end of your themes style.css file:

ul.twFeed li a:link, ul.twFeed  ul li a:visited, ul.twFeed
{
display: none;
color: #8c8c8c;
padding: 3px;
background-image: none;
}

(Untested and off the top of my head).