Vector orthogonal frequency division multiplexing (OFDM) is a promising modulation scheme, which allows for a flexible configuration and connects OFDM and single-carrier frequency domain equalization in a unified framework. In this letter, we design Alamouti-like space-time block coded and space-frequency block coded vector OFDM systems. Based on these schemes, we prove that, with two transmit and one receive antenna, the diversity order of the zero-forcing receiver is fixed to 2 over frequency selective fading channels, while that of the minimum mean square error receiver depends on the channel memory length, the vector block size, and the spectral efficiency.