Space-shift-keying (SSK) and spatial modulation (SM) enable multiple antenna transmission systems to convey information on antenna indices. While SSK/SM helps reduce the number of radio frequency (RF) chains, large numbers of antennas and low spatial correlations are required to achieve high data rates. This work investigates the use and design of multifunctional reconfigurable antennas (MRAs) for SSK/SM based transmission where a single-element MRA generates large numbers of modes. To enhance legacy SSK/SM performance while reducing RF hardware complexity, we propose single- and multi-carrier antenna mode-shift keying (MoSK) and mode modulation (MoM) schemes facilitated by MRAs. Based on an error probability analysis, we determine criteria for MRA design and mode set selection suitable for MoSK/MoM. We also develop two MRA designs and investigate their performances over Rayleigh fading channels. We argue that by creating MRA modes with low pattern correlations, channel correlations can be reduced to improve the detection performance. Extensive simulations demonstrate that MoSK/MoM performance exceeds that of SSK/SM along with significant complexity reduction. For instance, a single-carrier MoSK/MoM using a single MRA with 8 modes achieves about 2 dB gain compared to legacy SSK/SM requiring 8 antennas, and by multi-carrier MoSK/MoM using 4 subcarriers, an MRA with 32 modes can attain an error rate performance comparable to this single-carrier system.