In this paper, we propose an index modulated orthogonal frequency division multiplexing spread spectrum (IM-OFDM-SS) scheme, which combines the techniques of SS and IM under the framework of OFDM. In this scheme, the information bits are jointly conveyed by the indices of spreading codes and the conventional M-ary modulated symbols. A low-complexity maximal ratio combining (MRC) detector is designed, in which the receiver first detects the spreading codes and then de-spreads and demodulates the symbols. The bit error rate (BER) performance of IM-OFDM-SS systems in the presence of channel estimation errors is analyzed. An upper bound and approximate average bit error probability associated with maximum-likelihood and MRC detection, respectively, are derived. Subsequently, we extend the idea of IM-OFDM-SS to multi-code and multi-user scenarios, proposing generalized (G-)IM-OFDM-SS and IM-based multi-carrier code division multiple access (IM-MC-CDMA), respectively. Simulation results verify the analyses and show that the proposed IM/GIM-OFDM-SS outperforms the existing OFDM-IM and OFDM-SS schemes significantly. In addition, the IM-MC-CDMA exhibits a lower BER than MC-CDMA at the same SEs for either multi-user or single-user detection.