This paper proposes a cooperative space-time coding (STC) protocol, amalgamating the concepts of asynchronous cooperation, non-coherent detection as well as Distributed Turbo Coding (DTC), where neither symbol-level time synchronization nor CSI estimation is required at any of the cooperating nodes, while attaining a high performance even at low SNRs. More specifically, a practical cooperative differential space-time spreading (CDSTS) scheme is designed with the aid of interference rejection spreading codes, in order to eliminate the effect of synchronization errors between the relay nodes without the assistance of channel estimation or equalization. Furthermore, a set of space-time codewords are constructed based on Differential Linear Dispersion Codes (DLDC), which allows our CDSTS system to support an arbitrary number of relay nodes operating at a high transmission rate due to its flexible design. Rather than using conventional single-relay-assisted DTCs, novel multi-relay-assisted DTCs and a three-stage iteratively-decoded destination receiver structure are developed. In our simulations the system parameters are designed with the aid of EXIT chart analysis, followed by the characterization of the achievable BER performance for various synchronization delay values as well as for various diversity-multiplexing relationships in frequency-selective fast and/or quasi-static Rayleigh fading environments.