Rydberg sensors offer a unique approach to radio frequency (RF) detection, leveraging the high sensitivity and quantum properties of highly-excited atomic states to achieve performance levels beyond classical technologies. Non-linear responses and distortion behavior in Rydberg atom receivers are critical to evaluating and establishing performance metrics and capabilities such as spur-free dynamic range and tolerance to unwanted interfering signals. We report here on the measurement and characterization of non-linear behavior and spurious response of a Rydberg atomic heterodyne receiver. Single-tone and two-tone testing procedures are developed and implemented for measurement of harmonic and inter-modulation distortion in Rydberg atomic receivers based on multi-photon Rydberg spectroscopy and radio-frequency heterodyne signal detection and demodulation in an atomic vapor. For a predetermined set of atomic receiver parameters and RF carrier wave in the SHF band near-resonant to a cesium Rydberg transition, we measure and characterize atomic receiver selectivity, bandwidth, roll-off, compression point (P1dB), second-order (IP2) and third-order (IP3) intercepts, and spur-free dynamic range. Receiver intermodulation distortion is characterized for the case of an interfering signal wave applied at two frequency offsets relative to the near-resonant reference local oscillator, $ΔF/F= 10^{-4}$ at 6dB and $10^{-6}$ at 22dB single-tone bandwidths, respectively. We observe that under suitable operating conditions the atomic receiver can exhibit a suppression of harmonic and inter-modulation distortion relative to that of classical receiver mixer amplifiers. Finally, we describe how the non-linear behaviors of atomic receivers can provide unique, controllable RF signatures inaccessible by classical counterparts and propose their use to realize secure communication modalities and applications.