Part of the job of being a professional designer is that of instruction. In this case, the instruction consists of teaching your client that Word is not a viable graphics file format. It's a container format for text and images.
Reading between the lines, it sounds like what they really want are basic document templates (letterhead, invoices, etc) that feature the logo. If so, you can easily generate tiffs of the logo and place them into a nice template design in Word and provide that to them.
If, on the other hand, they really, honestly want raw logo art (for any future purpose) in a Word doc...well...you can certainly provide them with a Word doc with a placed, hi-rez tiff file that they can copy/paste to their heart's content. You can also export your AI art as a Windows MetaFile (.wmf) This way, the art will retain its vector information and you can place that into a Word doc, too. I don't think they will be able to do any sort of vector-level editing on it, though, without resorting to buying Illustrator.
I sympathize with your situation. I've actually had to deal with a similar request before. It's hard to explain to people about proper file formats when all they know is Word.