I'm about to design a (REST) API for a custom ERP solution. The API will then be connected to some EDI solution.
Are there some standards, common message format for contracts like placing orders, retrieving product catalog, prices, stocks, etc, or am I completely on my own?
So there isn't a widespread business message format tied to REST services in particular. However, as they work well with XML, I would recommend using UBL. It's an open standard and it's widely used in multiple international networks and it covers all typical message types so you shouldn't struggle to connect to EDI solutions using it.