I would like to sell a product that uses a device that is currently under patent. If I buy the device from the company and screw it onto my product, (which does something unrelated), can I sell it?
Unless there is some agreement with the supplier to the contrary (say a shrink-wrap license), you bought the device it and can whatever you like with it and not worry about patents the supplier has on the device itself. It is called "patent exhaustion".
From Wikipedia -
The exhaustion doctrine, also referred to as the first sale doctrine, is a U.S. common law patent doctrine that limits the extent to which patent holders can control an individual article of a patented product after a so-called authorized sale.
However, in doing so you may be infringing on patents other than patents the vendor has on the device itself. The vendor may have methods of use patents, someone other than the vender may have claims that read on the device itself, or the combination you are creating might infringe on a patent owned by someone completely unrelated to the vendor of the device.
I think this is mainly up to the terms of sale for the device that is patented. It is reasonable for a company to restrict their product from being used in an unintended way because they may face an increased liability. Your best bet is to simply contact the company and see if they will allow you to use their product as you desire.