Turning right off the Wye Bridge was the Salamanca Branch, which joined the Erie-Emporium line at Irvineton and left it again at Warren, ending at Olean. Turning left was the Chautauqua Branch, which turned north toward Corry, where it paralleled the Erie and then crossed it to head north to Brocton, NY, from where it paralleled the NKP to Buffalo. Both lines were previously the Western New York & Pennsylvania, later acquired by the PRR. From Brocton to Buffalo was operated as a double-track railroad, with westbound/southbound trains of both roads using the NKP main, the one closer to the lake, and all eastbound/northbounds using the PRR, on the land side, all traffic being dispatched by the NKP (which had many more trains). The line south from Oil City, formerly the Allegheny Valley Railroad, came up from Pittsburgh. As late as 1955, according to the Official Guide, there was a daily overnight Pittsburgh-Buffalo passenger train with a 12-Section 1-Drawing Room Pullman, with the two trains meeting at Oil City around 3 am (there had previously been a day train boasting a parlor car with broiler buffet, gone sometime before 1955); that was it for passenger service, and even the overnight had disappeared by 1961. After the expansion of Conway Yard around 1960 there was a daily through freight train from Buffalo to Conway and return via Corry, Oil City, and Pittsburgh (north side). Freight service lasted into the Penn Central, but I can't identify the actual abandonment dates after that.
