At my company, "Engineering Manager" does not seem to be a clearly defined role like the others. Usually the Architects help with technical decisions but also deal with more business value, while the Project Managers tell the Software Developers what to do.
Project Manager is the current term for what used to be "secretary."
Architect- Technical and implements solutions. Engineering Manager- usually tech or semi tech and manages people Project Manager- manages project, does not manage people. Typically creates documents, schedules, and tracks resources, budget, risk etc.
At my company, Engineering Manager leads work on the product (we have our own product), while Project Manager leads implementation/customization of product on client site. They are both considered less technical roles, while Architect is the technical guy (can be on product or implementation side).
Engineering Manager manages people. The other two do not