Why does my new furnace vibrate and smell like burnt oil?
My suggestion is to record the sound. If using your phone take a video. Move the phone slowly to knee height, up to head height, move over a couple of feet and repeat. 

It may be a piece of flashing in the air handler that is not sealing well any that can make a heck of a racket. As far as the smell again it could be a seal. Take note of the outside conditions when it is vibrating. Is it windy, raining, snowing?  If you can put together 1 or 2 more clues it may be easy to track it down.