Well you are showing infections. Evidence also of P2P file sharing which is an especially easy way to infect a computer, especially one not running an anti-virus program.
I hate to begin clean up this way but see no other option. Have not seen a log look like this with all these odd O1 entries.
Run HJT again and place a check mark next to all of the following entries;
R0 - HKLM\Software\Microsoft\Internet Explorer\Search,SearchAssistant =
R0 - HKLM\Software\Microsoft\Internet Explorer\Search,CustomizeSearch =
O1 - Hosts: <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
O1 - Hosts: "http://www.w3.org/TR/html4/loose.dtd">
O1 - Hosts: <html>
O1 - Hosts: <head>
O1 - Hosts: <script LANGUAGE="JavaScript">
O1 - Hosts: <!--
O1 - Hosts: if (window != top)
O1 - Hosts: top.location.href = location.href;
O1 - Hosts: // -->
O1 - Hosts: </script>
O1 - Hosts: <title>Site Unavailable</title>
O1 - Hosts: <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
O1 - Hosts: <style type="text/css">
O1 - Hosts: body{text-align:center;}
O1 - Hosts: .geohead {font-family:Verdana, Arial, Helvetica, sans-serif; font-size:10px;width:750px;margin:10px 0 10px 0;height:35px;}
O1 - Hosts: .geohead #geologo {width:270px;display:block; float:left; }
O1 - Hosts: .geohead #rightside {width:480px;display:block; float:right;border-bottom:1px solid #999999; height:27px;}
O1 - Hosts: .geohead #rightside #welcome {width:50%;display:block; float:left; text-align:left;}
O1 - Hosts: .geohead #rightside #wlinks {width:50%;display:block; float:right; text-align:right;}
O1 - Hosts: .ftr { margin:0px; color:#404040; font:x-small Arial,sans-serif; text-align:center; width:750px;}
O1 - Hosts: .bodywrap{display:block;height:470px;}
O1 - Hosts: .bodycnt{width:510px; display:block; float:left; background-color:#EEE9F5; height:auto; text-align:left; font-family:Arial, Helvetica, sans-serif;font-size:13px; color:#000000; padding:20px 20px 35px 20px;}
O1 - Hosts: .title { font-family:Arial, Helvetica, sans-serif; font-weight:bold; font-size:24px; color:#7C56A9}
O1 - …