Optoelectronic devices driven by terahertz (THz) waves have been used to control electron pulses, such as through acceleration, compression, and characterization of ultrashort pulsed electrons. In this study, we developed a THz generation setup with a lithium niobate crystal via the tilted-pump-pulse-front approach. Furthermore, a THz electro-optical sampling setup, an ultrashort pulsed electron generation system, and a THz streaking system with a simple butterfly-shaped THz optoelectronic resonator were also developed to determine the lower limits of THz intensities that can be used for characterization of picosecond pulsed electrons. Multiple deflections of the electron pulse occur when the duration is longer than the half cycle of the electric field at the THz optoelectronic resonator, which requires a higher THz intensity and makes the analyses difficult. The results obtained with appropriate analyses show that a weak THz field of a few kV/cm resonated with the THz optoelectronic device is sufficient to characterize picosecond pulsed electrons.