Lisboa Gare Oriente is a large Multi-modal Transport Hub located on the even larger Parque da Nações area which is a town in itself. Trust me, I've walked much of it.
Assuming your apartment is located at Calçada da Patriarcal,1250 Lisboa, (Google Maps), it is a long way from Gare Oriente, being situated of Avenida da Liberdade and running up towards the Rato Area.
If that indeed is where your apartment is, you would be much closer to Stª. Apolonia Station where the Lisbon to Porto trains depart from. A taxi will probably be the best way to get to the station, unless you are very close to the Avda. Liberdade end. There, you could just walk to the Avenida Metro Station and the metro to Stª Apolonia.
