Not sure I fully understand what you want to do but here is a sample code that should help you get started. I strongly suggest you have a look at XPATH to understand it.

        HtmlDocument doc = new HtmlDocument();
        doc.Load(yourFile);

        // get all TR with a specific class name, starting from root (/), and recursively (//)
        foreach (HtmlNode node in doc.DocumentNode.SelectNodes("//tr[@class='tblDataGreyNH' or @class='tblDataWhiteNH']"))
        {
            // get all TD below the current node with a specific class name
            HtmlNode inOrOut = node.SelectSingleNode("td[@class='tblHeader']");
            if (inOrOut != null)
            {
                string io = inOrOut.InnerText.Trim();
                Console.WriteLine(io.ToUpper());
                if (io.Contains("Time"))
                {
                    // normalize-space gets rid or whitespaces (\r,\n, etc.)
                    // text() gets the node's inner text
                    foreach (HtmlNode td in node.SelectNodes("td[normalize-space(@class)='' and normalize-space(text())!='' and normalize-space(text())!='00:00']"))
                    {
                        Console.WriteLine("value:" + td.InnerText.Trim());
                    }
                }
            }

            // gets all TD below the current node that define the NOWRAP attribute
            HtmlNodeCollection tdNoWraps = node.SelectNodes("td[@nowrap]"); 
            if (tdNoWraps != null)
            {
                foreach (HtmlNode tdNoWrap in tdNoWraps)
                {
                    string value = tdNoWrap.InnerText.Trim();
                    if (value == string.Empty)
                        continue;

                    Console.WriteLine("value:" + value);
                }
            }
        }

It will output this from your sample page:

IN
value:7:47
value:7:46
value:7:45
value:7:51
OUT
value:15:35
value:15:33
value:12:38
value:8:59
IN
value:12:38
value:8:59
OUT
value:15:35
TOTAL TIME
value:07:48
value:07:47
value:07:50
value:01:08
REGULAR TIME
value:07:48
value:07:47
value:07:50
value:01:08