Thanks for all the great responses! I didn't realize that people around the country would join in this conversation.
I plugged the fan into an extension cord and the same loud noise still occurred.
I believe that this ruled out mounting noise and binding/housing noise. The fan was mounted on only one stud, but I don't think that was causing the problem, since it still made the sound when it was out of the ceiling.
The handyman that did the instillation vented the fan to the attic (no external venting). Several posts have suggested that this was not a good idea. However, it was vented to the attic for 15 years before fan #2 was installed, so it seems like it would still be OK. I went up to the attic 3 years ago and saw no problems. What are the risks of not venting outside of the house? How expensive would external venting be?
Are there any NuTone 110 DIY oiling/repairs that I could do? Any instructions? This would be ideal, if feasible.
If I need to replace the fan, how much should I expect to pay? I would pick up the new fan/mounting kit and have them mounted. How can I find someone qualified to this this right at a fair price? I don't want to revisit this for 15+ years. Any other suggestions?