The aircraft taxied for departure to Sydney about 90 minutes behind schedule due to fog at Wagga. Although the First Officer was the handling pilot for the flight, the Captain taxied the aircraft as it was not fitted with dual nose wheel steering controls. During taxy, the First Officer read the pre-takeoff checklist. At the flight and navigation instruments check, he incorrectly read the outbound track from the flight plan as 118, which was the distance in nautical miles from Wagga to the TAPIO reporting point enroute to Sydney. The correct track was 053 degrees magnetic and as neither pilot had recognised the error, they set 118 on both HSI's. After issuing an airways clearance for the aircraft to proceed to Sydney via Bindook at 9,000 ft, the Wagga tower controller cleared the aircraft to takeoff on runway 05 and to make a right turn. The First Officer assumed the handling pilot duties when the Captain handed over control of the aircraft during the takeoff roll. The tower controller, who was monitoring the departure, said he lost sight of the aircraft due to low cloud while it was maintaining runway heading. Following a request from the tower controller the Captain advised that the cloud base was 1,000 ft above terrain. When the aircraft was established on the 118 radial of the Wagga VOR, the Captain passed the departure message. He advised the tower controller that the aircraft was tracking 053, which he read correctly from the flight plan, and was climbing to 9,000 ft. At cruising altitude the aircraft was above two layers of cloud, through which the crew had occasional glimpses of the ground. About 10 minutes after departure the Captain decided to climb to FL 110 due to moderate turbulence, and to avoid cloud build-ups ahead. ATC requested the crew to squawk code 1000 with ident prior to issuing a clearance for the change of level. The aircraft was then located 70 NM to the right of the planned track, to the south west of Canberra. This error was subsequently recognised by the Captain who advised ATC. The aircraft was issued with a clearance to track via Canberra and Bindook to Sydney. There was no confliction with other IFR traffic. Significant Factors. The First Officer misread tracking information from the flight plan during the pre-takeoff checks. Neither pilot verified the orientation of the selected track by reference to the appropriate map or chart. Weather conditions prevented the tower controller from adequately monitoring the aircraft's outbound track.