A novel technique, two-dimensional (2D) polarization single-molecule imaging, is presented. It is based on measurements and analysis of fluorescence intensity as a function of excitation and emission polarization angles. The technique allows recording of full information on the steady-state polarization properties of fluorescent objects. It is particularly suitable for application to single multichromophoric systems (molecules or nanoparticles) with energy transfer (ET) between different chromophores (e.g., single fluorescent pi-conjugated polymer chains). The 2D polarization data simultaneously provide information on the conformation of the system and the efficiency of its internal excitation ET. The technique is used to characterize single chains and different kinds of chain aggregates of different conjugated polymers at different temperatures. The 2D polarization measurements reveal a dramatic difference in ET taking place in these systems. Clear temperature dependence of ET is observed for individual aggregates as well as for their statistical ensembles. Also, a dependence on solvent and aggregate size is shown. Additionally, extensive "traditional one-dimensional" polarization results on the polarization anisotropy of fluorescence excitation and emission are presented. These results and findings are discussed in relation to internal organization of the nano-objects under study.