In this article, we introduce intensity modulation and direct detection compatible enhanced optical-orthogonal frequency division multiplexing with index modulation (EO-OFDM-IM) schemes. These approaches augment the spectral efficiency (SE) relative to classical counterparts by enlarging the index domain information using the so-called virtual sub-carriers. The classical O-OFDM-IM schemes do not necessarily enhance the SE because of low cardinality of IM complex-valued sub-carrier set which is limited by constraints like Hermitian symmetry. The index domain extension for EO-OFDM-IM schemes is achieved by replacing the complex-valued sub-carriers (as in O-OFDM-IM) by twice real-valued virtual sub-carriers. The realization of non-negative signals is based on precepts of classical O-OFDM approaches, that are direct current (DC) O-OFDM and asymmetrically clipped (AC) O-OFDM. Thus, we refer to the EO-OFDM-IM approaches as DCEO-OFDM-IM and ACEO-OFDM-IM. We shall establish that in addition to improving SE, EO-OFDM-IM schemes provide extended granularity effectuating better SE/energy efficiency (EE) trade-off and improved bit error rate performance over classical counterparts. The EO-OFDM-IM schemes, however, are suitable for lower alphabet cardinalities of pulse-amplitude modulation making it difficult to attain high spectral efficiencies while maintaining EE. To circumvent this limitation, dual-mode (DM) counterparts, DCEO-OFDM-DM and ACEO-OFDM-DM are proposed. The numerical simulations shall demonstrate that the EO-OFDM-DM approaches are more energy and spectral efficient than classical O-OFDM-DM schemes and provide an advantageous granularity for EE/SE trade-off. Additionally, we use efficient index mapping and de-mapping algorithms based on Pascal's triangle, which allows investigating these approaches for peak SE by precluding the so-called sub-block partitioning. For peak SE, the use of optimal maximum-likelihood (ML) detector is cumbersome, therefore, we introduce two sub-optimal low-complexity detectors based on energy detection and ML criterion. INDEX TERMS Optical-orthogonal frequency-division multiplexing, index modulation, intensity modulation and direct detection, optical wireless systems.