Optoelectronic properties of site-controlled AlGaAs/GaAs quasi-one-dimensional structures are investigated. Controllable linear variation of the band gap along the vertical axis of the quantum wire, symmetrical with respect to its center, results in a set of closely separated (by a few meV) confined electron and hole states giving rise to multiple excitonic lines well resolved in the photoluminescence spectra. Exciton recombination and relaxation dynamics in this multilevel system is studied by time-resolved and photon correlation spectroscopy and described with a master-equation model. Increasing carrier occupation in the higher-energy levels results in appearance of new multiexciton lines in the emission from the lowest-energy states. Typical features of quantum dot multiexciton dynamics such as antibunching photon statistics and cascaded biexciton-exciton emission are observed for the ground state. Pronounced bunching photon statistics and strong temporal correlations between photons emitted from the different excited states indicate sequential photon emission from multiple discrete energy levels. These structures thus represent a class of quasi-one-dimensional systems with tailored energy levels and photon emission statistics.