Never c & p from a rich text editor. If you must use it, 1st c & p into Notepad, then into WordPress.
Notepad strips all the extraneous tags inputed by rich text editors.
I agree with samboll. Never use a full-blown word processor (OpenOffice Writer, Word, WordPerfect, WordPad, etc) to cut and paste your text. These all have formatting commands built in that get pasted with the text.
There are a few options:
You can use Notepad like samboll suggests. It does just what he says. It is rather limited, though. For editing text files, I use PS Pad – it works well and it has spellcheck and other options that Notepad doesn’t have. It is a code editor, but can be used as a Notepad replacement.
You can use a tool like w.bloggar or Zempt to type your posts on your local PC and them publish them to your blog. You won’t even have to cut and paste as these tools have publishing capability. You will have to configure the tools to work with your blog, though.
You can change the settings for the built-in WP post editor so that it displays more lines. In the Admin Panel, go to Options – Writing and change the number of lines to a larger number.
