We present the optical and UV emission-line properties of 160 X-ray-selected active galactic nuclei (AGN) taken from the RIXOS survey (including Hα, Hβ, [Oiii] lambda5007, Mgii lambda2798 and Ciii] lambda1909). This sample is believed to contain a mixture of absorbed and unabsorbed objects, with column densities up to ~4x10^21cm^-2. Although the distribution of the [Oiii] lambda5007 EW for the RIXOS AGN is typical of optically selected samples, the Balmer line EWs are relatively low. This is consistent with the presence of a dust absorber between the broad- and narrow-line regions (e.g. a molecular torus), and intrinsically weak optical line emission. We find Baldwin effects in Ciii] lambda1909 and Mgii lambda2798, and a positive response of the Mgii line to its ionizing continuum. There is a strong correlation between the EW and FWHM of Mgii, which may be similar to that seen in other samples for Hβ. We demonstrate that this is consistent with models that suggest two line-emitting zones, a `very broad-line region' (VBLR) and an `intermediate-line region' (ILR). The correlation between EW and FWHM in Mgii may be a physical characteristic of the ILR: e.g. the radiative acceleration of the line-emitting clouds; or it may reflect a geometric dependence, e.g. anisotropies in the line or continuum emission, or a smaller covering factor of the ILR at large distances. We found no correlation between the Hβ FWHM and the slope of the X-ray spectrum, despite reports of correlations in other samples. However, this may be due to the effects of dust absorption, which suppresses the broad Hβ component, masking any relationship. The Hα FWHM does tend to be narrow when alpha_x is soft, and broadens as alpha_x hardens, although the formal probability for this correlation is low (91 per cent). If the distribution of alpha_x in the RIXOS sample reflects the level of intrinsic absorption in these AGN, the data suggest a possible link between the velocity of the Balmer line-emitting region and the amount of absorbing material beyond.