could this be done with Openssl, but instead of attacking a file, attacking a mounted drive?
I am afraid that I do not quite understand that. As far as I am aware SSL is a communications protocol, and I do not see the relationship to cracking an encrypted and password protected drive?

also how would you find what type of encryption was used, and the strength.. or you just picked one and hope to guess it
That should be in the manual or on the manufacturer's website. I am not aware of any USB sticks that offer more than one, although different sticks have different (default) solutions. A Google search for the make and model might also turn up some product reviews that would contain those technical details.

If you look at the very interesting article that SirDice has linked to, you will see that the answers to your questions are dependent on particular products/implementations and how the user has applied them. It also raises some questions of clarification regarding your original question:

1. What resources are available ( i.e. what is your attack processing power)?
2. What is an acceptable timescale for the product to resist or be cracked in?
3. Is this a destructive or non-destructive scenario?.......... crudely speaking: "can we take the thing apart?"
4. Can we assume the availability of specialist equipment and competent electronic enginering technician's skills?
5. How long and strong is the password assumed to be?