Is there a private party room or area that will accommodate a larger work party like approximately 20 people

No room. No tables bigger than 4 or 6. If your party is bigger they can seat u in adjacent ones, but wont move them to sit together (its impossible bc they are static).

What is the cost for the room?

No

No. There is a patio outside. Maybe that would work?

Not that I've seen. I've only been there 2x though.