The 2Jy sample is a survey of radio galaxies with flux densities above 2 Jy at 2.7 GHz. As part of our ongoing work on the southern subset of 2Jy sources, in paper I of this series we analysed the X-ray cores of the complete 2Jy sample with redshifts 0.05 < z < 0.7. For this work we focus on the X-ray emission associated with the extended structures (jets, lobes, and environments) of the complete subset of 2Jy sources with 0.05 < z < 0.2, that we have observed with Chandra. We find that hotspots and jet knots are ubiquitous in FRII sources, which also inhabit systematically poorer environments than the FRI sources in our sample. Spectral fits of the hotspots with good X-ray statistics invariably show properties consistent with synchrotron emission, and we show that inverse-Compton mechanisms under-predict the X-ray emission we observe by 1-2 orders of magnitude. Inverse-Compton emission is detected from many of the lobes in our sample, and we find that the lobes of the FRII sources show magnetic fields lower by up to an order of magnitude than expected from equipartition extrapolations. This is consistent with previous results, which show that most FRII sources have electron energy densities higher than minimum energy requirements.cores of the 2Jy sources in the subset of Dicken et al. (2008), using data from Chandra and XMM-Newton, and found our results to be in good agreement with those of Hardcastle et al. (2006Hardcastle et al. ( , 2009 on the 3CRR radio galaxies.In this work we focus on the extended X-ray emission (jets, hotspots, and lobes) and the environments of the 0.05 < z < 0.2 subset of sources that we have observed with Chandra, whose nuclei we studied in paper I. Our knowledge of X-ray jets (see e.g. the review by Worrall 2009) and hotspots (e.g. Hardcastle et al. , 2007bMassaro et al. 2010Massaro et al. , 2015 has certainly improved over the last two decades, as has our understanding of the environment in which radio galaxies live (e.g. Belsole et al. 2007;Croston et al. 2008;Ineson et al. 2013Ineson et al. , 2015, but the samples of radio galaxies with available detailed observations are still relatively small, and more work needs to be done to understand their extended structures and how they co-evolve with the hosts (see also the recent review by Tadhunter 2016). The 2Jy sample is important in that it is not only statistically complete, but uniformly observed, with c 0000 The Authors