We report on searches for neutrino sources at energies above 200 GeV in the Northern sky of the Galactic plane, using the data collected by the South Pole neutrino telescope, IceCube, and AMANDA. The Galactic region considered in this work includes the local arm toward the Cygnus region and our closest approach to the Perseus Arm. The searches are based on the data collected between 2007 and 2009. During this time AMANDA was an integrated part of IceCube, which was still under construction and operated with 22 strings (2007-2008) and 40 strings (2008-2009) of optical modules deployed in the ice. By combining the advantages of the larger IceCube detector with the lower energy threshold of the more compact AMANDA detector, we obtain an improved sensitivity at energies below ~10 TeV with respect to previous searches. The analyses presented here are a scan for point sources within the Galactic plane, a search optimized for multiple and extended sources in the Cygnus region, which might be below the sensitivity of the point source scan, and studies of seven pre-selected neutrino source candidates. For one of them, Cygnus X-3, a time-dependent search for neutrino emission in coincidence with observed radio and X-ray flares has been performed. No evidence of a signal is found, and upper limits are reported for each of the searches. We investigate neutrino spectra proportional to E–2 and E–3 in order to cover the entire range of possible neutrino spectra. The steeply falling E–3 neutrino spectrum can also be used to approximate neutrino energy spectra with energy cutoffs below 50 TeV since these result in a similar energy distribution of events in the detector. For the region of the Galactic plane visible in the Northern sky, the 90% confidence level muon neutrino flux upper limits are in the range E 3 dN/dE ~ 5.4-19.5 × 10–11 TeV2 cm–2 s–1 for point-like neutrino sources in the energy region [180.0 GeV-20.5 TeV]. These represent the most stringent upper limits for soft-spectra neutrino sources within the Galaxy reported to date.