Meson production in proton-deuteron collisions has been studied using the WASA detector facility at the CELSIUS storage ring in Uppsala. Data were obtained at two different beam energies, 1360 MeV and 1450 MeV, slightly above threshold for η and ω mesons. The differential cross sections of pd → 3He ω constitute the first measurements of this reaction covering the whole angular range. The ω angular distributions are isotropic at 1360 MeV but have strong forward and backward enhancements at 1450 MeV. Theoretical calculations using a two-step model fail to reproduce the shapes of the angular distributions and underestimate the total cross sections. The tensor polarisation of the ω meson has been derived from the measured angular distributions of the ω decay products. The π+ π- π0 and the π0 γ decay channels gave consistent results, showing that the ω meson is produced unpolarised at both energies. This is in contrast to a recent MOMO measurement which showed that the Φ meson is produced almost completely polarised in the pd → 3HeΦ reaction. Different production dynamics of ω and Φ mesons close to threshold raises the question whether the Okubo-Zweig-Iizuka (OZI) rule is applicable in low-energy nucleon-nucleon reactions. The angular distributions of the η meson produced in the pd → 3He η reaction are strongly enhanced for forward going η mesons at both energies. The σ(pd → 3He π+ π- π0 )/σ(pd → 3He π0 π0 π0 ) ratio has been measured and discussed in terms of isospin amplitudes. A rough estimate of the pd → 3He π0 π0 π0 π0 cross sections has also been obtained and the pd → 3He η π0 reaction has been studied for the first time near threshold.