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We perform a sensitive (line confusion limited), single-side band spectral survey towards Orion KL with the IRAM 30m telescope, covering the following frequency ranges: 80-115.5GHz, 130-178GHz, and 197-281GHz. We detect more than 14400 spectral features of which 10040 have been identified up to date and attributed to 43 different molecules, including 148 isotopologues and lines from vibrationally excited states. In this paper, we focus on the study of OCS, HCS⁺, H₂CS, CS, CCS, C₃S, and their isotopologues. In addition, we map the OCS J=18-17 line and complete complementary observations of several OCS lines at selected positions around Orion IRc2 (the position selected for the survey). We report the first detection of OCS ν₂=1 and ν₃=1 vibrationally excited states in space and the first detection of C₃S in warm clouds. Most of CCS, and almost all C₃S, line emission arises from the hot core indicating an enhancement of their abundances in warm and dense gas. Column densities and isotopic ratios have been calculated using a large velocity gradient (LVG) excitation and radiative transfer code (for the low density gas components) and a local thermal equilibrium (LTE) code (appropriate for the warm and dense hot core component), which takes into account the different cloud components known to exist towards Orion KL, the extended ridge, compact ridge, plateau, and hot core. The vibrational temperature derived from OCS ν₂=1 and ν₃=1 levels is ≃210K, similar to the gas kinetic temperature in the hot core. These OCS high energy levels are probably pumped by absorption of IR dust photons. We derive an upper limit to the OC₃S, H₂CCS, HNCS, HOCS⁺, and NCS column densities. Finally, we discuss the D/H abundance ratio and infer the following isotopic abundances: ¹²C/¹³C=45±20, ³²S/³⁴S=20±6, ³²S/³³S=75±29, and ¹⁶O/¹⁸O=250±135.