This question is best posted to the classic and vintage forum. The posters there have way more experience than I do.
That said, I think yours was probably built early to mid 80s, since it has the Piaggio sticker on it. I'm guessing it was made in Japan. You can tell for sure if the bottom bracket measures 68 mm across. What are the brands of the components? (Shifters, derailers, etc) That will help to pinpoint the age as well.
700 x 32c denotes the tire size. That's a common road tire size, and it doesn't generally change with the bike size. As for frame size, you'll just have to measure it youself.
And finally, if you do re-post over to the classic and vintage forum, it helps to have a drive-side picture of your bike (so the nice guys and gals can see the derailluers).
It really does look like a cyclocross bike, especially with those brakes and all that clearance between the front wheel and the fork. But I didn't think cross bikes were made 20 years ago? Maybe it's an older frame re-purposed for cross racing. Or more likely, it's a touring bike frame.