We have a need to import orders from Episerver into an external system, this does not need to be done real-time and will be a service running on a different server. I would like to use the Episerver/Mediachase objects to do that, but am having trouble figuring out how to initalize the OrderContext and pull data from the Episerver database. What is the best way to use the commerce objects outside of the episerver website soluction/project?
I do not suggest using EPiServer/Mediachase objects outside EPiServer Commerce website. Better create DTO objects and some thin anticorruption layer between EPiServer and your other system.
Look at https://github.com/Geta/service-api it translates EPiServer/Mediachase objects to DTO objects. This way you also control what you want to share and what not and you can enrich your DTO object with additional data as you need.