Просто удалите первые 11 букв или символов из строки:
String startTag = "<sessionid>";
String endTag = "</sessionid>";
if (startTag.equalsIgnoreCase("<sessionid>") &&
endTag.equalsIgnoreCase("</sessionid>"))
{
int startLocation = strResponse.indexOf(startTag);
int endLocation = strResponse.indexOf(endTag);
Log.i("StartLocation", ""+startLocation);
Log.i("EndLocation", ""+endLocation);
String session_id = strResponse.substring(startLocation, endLocation);
session_id = session_id.substring(11, session_id.length());
ConstantData.session_id =session_id;
Log.i("SessionId", ""+session_id);
}