Most of the Galactic center (GC) gas moves in nearly circular orbits in a nuclear ring (hereafter the Galactic center ring, GCR). This is the case of cloud complexes such as Sgr A or Sgr B, where the gas is dense, warm and exhibits a rich molecular chemistry. The origin of these properties is thought to be shocks, in particular due to the large scale dynamics of the Galaxy. In addition, there are gas clouds moving in highly non-circular orbits known from observations of low density tracers such as CO(1-0). The physical conditions of the clouds moving with non-circular velocities are not well known. We have studied the physical conditions of the gas in non-circular orbits to better understand the origin of the unusual physical conditions of the GC molecular gas and the possible effect of the large scale dynamics on these physical conditions. Using published CO(1-0) data, we have selected a set of clouds belonging to all the kinematical components seen in the longitude-velocity diagram of the GC. We have carried out a survey of dense gas in all the components using the J=2-1 lines of CS and SiO as tracers of high density gas and shock chemistry. We have detected CS and SiO emission in all the kinematical components. The gas density and the SiO abundance of the clouds in non-circular orbits are similar to those in the GCR. Therefore, in all the kinematical components there are dense clouds that can withstand the tidal shear. However, there is no evidence of star formation outside the GCR. The high relative velocity and shear expected in the dust lanes along the bar major axis could inhibit the star formation process, as observed in other galaxies. The high SiO abundances derived in the non-circular velocity clouds are likely due to the large-scale shocks that created the dust lanes.