This paper investigates multiuser orthogonal space-time block coded signal detection within the ordered successive interference cancellation (OSIC) framework. Both the zero-forcing and minimum-mean-square-error ordering criteria are considered. When each user terminal is equipped with no more than four transmit antennas, it is shown that orthogonal transmit redundancy leads to an appealing signal ordering property: in each processing layer the transmitted symbols of an arbitrary user are associated with an identical ordering metric. This guarantees the feasibility of (user based) group-wise symbol recovery through the OSIC mechanism. Analytic bit-error-rate performance is given. Computer simulations and flop count evaluations are also provided for comparing the OSIC based solution with existing multiuser detection schemes reported for the considered system.