This paper is concerned with the nonlinear behaviors of acoustic waves produced by two degrees-of-freedom rigid oscillators containing nonlinearities and immersed in infinite fluid medium. The vibrations of the oscillators are computed by both the harmonic balance method (HBM) and the direct-time integration scheme, whereas the linearized Euler equations (LEEs) of the acoustic fluid are discretized by a fourth-order dispersion-relation-preserving (DRP) scheme in space and a four-level explicit time marching scheme in time. A constrained moving least-squares (CMLS) immersed boundary method (IBM) is used to enforce the boundary conditions on the common interfaces of the rigid oscillators and the Cartesian grid of the acoustic fluid. A serially staggered procedure is adopted to solve the governing equations of the oscillators and the acoustic fluid as a coupled system. The perfectly matched layer (PML) technique is utilized to damp out the out-going acoustic waves on the boundaries of the truncated computational domain to approximate the nonreflecting wave conditions. Physical insights into the mechanism of the nonlinear acoustic waves induced by super-harmonic resonances, principal resonances, internal resonances, and combination resonances of two degrees-of-freedom nonlinear oscillator systems are provided. The interference fringes of the acoustic waves due to the nonlinear vibration of the system are also discussed. Numerical results show that the sound fields radiated from the vibration system with the above nonlinear behaviors exhibit more complicated interference phenomena since the high-order harmonic components are introduced.