This dataset explores both the internal and external atomic degrees of freedom to observe quantum entanglement between the modes produced by a mirrorless optical parametric oscillator operating below the oscillation threshold in a sample of free-space cold cesium atoms. Using a new heterodyne technique, we recover the covariance matrix that reveals the quantum entanglement for two different pairs of modes, thus demonstrating the generation of four entangled modes in this system. Applications to quantum networks and the possibilities of studying higher orders of entanglement are a direct consequence of the present study.