If you can't read the msg files in a plain text editor (like a notepad type program) they probably saved as HTML files (it depends on how Outlook is set up). There's no specific viewer for that in Android that I know of, but you might try opening the file in an app used to open office documents.
The other alternative is to get a program that runs on your computer to convert the files to plain text, then view those on your phone. Or you could, of course, just learn enough HTML to ignore the tags and read the text.