[1] No 'city' called Osrhoene is known. Rather, the region of Osrhoene (see below) had as its capital the city of Edessa, present-day Urhai. The city was also called 'Orroene' in Greek, 'Orrei/Orrhei' in Latin. See OCD4 Edessa.
[2] Osrhoene was a region of NW Mesopotamia (present-day Syria/Turkey). It broke away from the Seleucids around 100 BCE and was a buffer state between the Roman and Parthian empires, but eventually became Roman. Cf. phi 827, and see generally OCD4 Osroene.
[3] Osrhoes was an Iranian name. Besides the eponymous founder of Osrhoene, it was most famously borne by the Parthian king Osrhoes (109-128) who was at war with Trajan and at peace with Hadrian. See alpha 3128.