If you are doing it from Word, the easiest way would be to open the text file in Word and use Word's search functionality. That way you don't need to implement your own search functionality.
Just record a macro of this action: Open a text file in Word and search for a specific string (Ctrl-F). The result looks something like this:
Sub Macro1()
    Documents.Open FileName:="YourFile.txt", ConfirmConversions:=False, _
        ReadOnly:=False, AddToRecentFiles:=False, PasswordDocument:="", _
        PasswordTemplate:="", Revert:=False, WritePasswordDocument:="", _
        WritePasswordTemplate:="", Format:=wdOpenFormatAuto, XMLTransform:="", _
        Encoding:=1252
    Selection.Find.ClearFormatting
    With Selection.Find
        .Text = "YourSearchText"
        .Replacement.Text = ""
        .Forward = True
        .Wrap = wdFindContinue
        .Format = False
        .MatchCase = False
        .MatchWholeWord = False
        .MatchWildcards = False
        .MatchSoundsLike = False
        .MatchAllWordForms = False
    End With
    Selection.Find.Execute
    If Not Find Is Nothing Then
        ' your action here '
    End If
End Sub
You can then edit the recorded macro to suit your needs.
Edit: I see that I partly misunderstood your question. My answer only covers how to search a text file for a specific string, not how to search the file system for a list of files.