As long as there is an API service that can be used to send/receive messages, then you can integrate with MX and automate workflow solutions. EPICOR does offer this.
The following youtube video Accessing the Epicor REST API - YouTube shows that you can access their RESTAPI documentation from a running instance where you have detailed information on what is needed to GET/POST.. between the different exposed services. (I tried to find the stand-alone- documentation online but was unsuccessful).
I also saw that there are quite a few companies and products that help facilitate the integration with this platform. So, it's definitely possible and profitable :)
You can also look into using an ODATA API service like the one from CDATA (OData Service Epicor ERP: OData Epicor ERP API - CData Software). You can connect to CData following the guidelines from this resource, CData Connect Cloud - Mendix
As for OMNIWIN, I couldn't find anything useful about integrations with other applications. Their FAQ talks a lot about digitalisation, pretty much every question :) so I hope a web service that allows for exchanging of messages is included. I would contact them directly and ask what options they have available for allowing instructions to be received from external applications.