We consider the problem of monostatic radar sensing with orthogonal frequency-division multiplexing (OFDM) joint radar-communications (JRC) systems in the presence of phase noise (PN) caused by oscillator imperfections. We begin by providing a rigorous statistical characterization of PN in the radar receiver over multiple OFDM symbols for free-running oscillators (FROs) and phase-locked loops (PLLs). Based on the delay-dependent PN covariance matrix, we derive the hybrid maximum-likelihood (ML)/maximum a-posteriori (MAP) estimator of the deterministic delay-Doppler parameters and the random PN, resulting in a challenging high-dimensional nonlinear optimization problem. To circumvent the nonlinearity of PN, we then develop an iterated small angle approximation (ISAA) algorithm that progressively refines delay-Doppler-PN estimates via closed-form updates of PN as a function of delay-Doppler at each iteration. Moreover, unlike existing approaches where PN is considered to be purely an impairment that has to be mitigated, we propose to exploit PN for resolving range ambiguity by capitalizing on its delay-dependent statistics (i.e., the range correlation effect), through the formulation of a parametric Toeplitz-block Toeplitz covariance matrix reconstruction problem. Simulation results indicate quick convergence of ISAA to the hybrid Cramér-Rao bound (CRB), as well as its remarkable performance gains over state-of-the-art benchmarks, for both FROs and PLLs under various operating conditions, while showing that the detrimental effect of PN can be turned into an advantage for sensing.