the point of EF is to map database query column values to defined POCO objects. while you could use compiler services to create the dbcontext object at runtime, you would need to use reflection to access it properties.
it is probably easier to to use native adodb/sqlclient, and load the 3 tables into a custom collection, as you will need custom code to access anyway.
your other alternative, is to use a json, or xml column for the custom fields.