Link opens a new website instead of my own

I have copied the generated code from your website. The new window happens because of the target="_blank" in the anchor a tag. If you can check the widget code/settings you would know if you need to change PHP code or is configurable.

<div class="socialmedia-buttons smw_left">
<a href="https://www.facebook.com/pages/Volunteering-News/391260697641619" rel="nofollow" target="_blank">
<img width="32" height="32" src="http://www.volunteeringnews.com/wordpress/wp-content/plugins/social-media-widget/images/cutout/32/facebook.png" alt="Follow Us on Facebook" title="Follow Us on Facebook" style="opacity: 0.8; -moz-opacity: 0.8;" class="fade">
</a>
<a href="https://plus.google.com/u/0/b/107875899230242366723/107875899230242366723/posts" rel="publisher" target="_blank">
<img width="32" height="32" src="http://www.volunteeringnews.com/wordpress/wp-content/plugins/social-media-widget/images/cutout/32/googleplus.png" alt="Follow Us on Google+" title="Follow Us on Google+" style="opacity: 0.8; -moz-opacity: 0.8;" class="fade">
</a>
<a href="https://twitter.com/volunteeringnew" rel="nofollow" target="_blank">
<img width="32" height="32" src="http://www.volunteeringnews.com/wordpress/wp-content/plugins/social-media-widget/images/cutout/32/twitter.png" alt="Follow Us on Twitter" title="Follow Us on Twitter" style="opacity: 0.8; -moz-opacity: 0.8;" class="fade">
</a>
</div>

EDIT: As per the widget’s page you can configure it under widget settings. It can be found usually under appearance->widgets.