In scenarios where wide-amplitude shock excitation is encountered, a routine bistable configuration struggles to achieve satisfactory energy transfer, and a sensible combination of multiple nonlinear oscillators with different stiffness mechanisms can be exploited to achieve optimal vibration mitigation performance. In this paper, a nonlinear energy conversion and multi-stiffness combination inspired dynamic vibration absorber (NECMC-DVA) is proposed with a magnetic-spring tunable nonlinear stiffness element as the substructure. Parametric studies are performed for different modes of magnet-spring tunable nonlinear stiffness unit arrays considering transient impulses and harmonic excitation. The NECMC-DVA device, which comprises bistable oscillators, cubic stiffness oscillators, and hybrid stiffness oscillators, is also experimentally demonstrated for its synergistic performance in vibration mitigation and energy harvesting. The performance of the NECMC-DVA is measured under transient impulses and harmonic excitations. It has been found that the NECMC-DVA, which consists of a bistable oscillator, a cubic stiffness oscillator, a hybrid stiffness oscillator, energy-capture elements, and motor sequences, achieves high-efficiency nonlinear energy transfer and significant shock robustness in wide-amplitude impulsive scenarios. The NECMC-DVA with hybrid energy sinks demonstrates more remarkable targeted energy transfer and energy conversion performance than its pure bistable oscillator counterpart. Furthermore, the NECMC-DVA prototype can achieve adaptive vibration control modulation and energy conversion management through motion control boards by monitoring ambient excitation signals. Therefore, the NECMC-DVA enables integrated active and passive mitigation and energy harvesting to simultaneously accommodate multi-source indeterminate vibration and shock environments.