Actually I have no idea how to answer most of your questions.
Let's try to find some more details.
When I start Trados it says Trados 2007.
That's Trados version 8.x - if you look at Help - About... in the Workbench application window, you can see the exact version. (In fact, this is where you find the version info for pretty much every Windows-based software.)
My Word programm is pretty old.
Again, please have a look under Help (or "?") - About... .
I'm translating in word, not rtf.
Certainly - "RTF" is not an application, but a format ("Rich Text Format"). In fact, Trados uses RTF to interface with Word.
In the TM, I select "Clean up" in "Tools". Then I add the file that I want cleaned. At the bottom of the window it then says "Converting DOC-RTF", which I don't know why it does that, because then it says it can't process rtf, also there at the bottom of the window.
Trados needs to convert the .doc file into RTF to run the cleanup process - the message indicates that this conversion fails. This may have numerous causes.
I tried to convert it into rtf and translate it from there, then clean it up.
That actually worked, but it made the files so big, that I have to convert them back into .doc. When I do that, the whole formatting is messed up.
The increase in file size is normal, particularly if the document contains graphics.
Oh, and I have never heard of Tw4WinClean.Main and can't find it on my computer either. What is that?
It's a Word macro installed with Trados, which allows you to 'manually' force cleanup - please use the forum search to find more details (this has been discussed on numerous occasions).
Looks like you can use the macro to clean up the Word file (hopefully without any formatting issues), and the normal cleanup process to clean the RTF copy (to update your TM).