IoT networks often face conflicting routing goals such as maximizing packet delivery, minimizing delay, and conserving limited battery energy. These priorities can also change dynamically: for example, an emergency alert requires high reliability, while routine monitoring prioritizes energy efficiency to prolong network lifetime. Existing works, including many deep reinforcement learning approaches, are typically centralized and assume static objectives, making them slow to adapt when preferences shift. We propose a dynamic and fully distributed multi-objective Q-learning routing algorithm that learns multiple per-preference Q-tables in parallel and introduces a novel greedy interpolation policy to act near-optimally for unseen preferences without retraining or central coordination. A theoretical analysis further shows that the optimal value function is Lipschitz-continuous in the preference parameter, ensuring that the proposed greedy interpolation policy yields provably near-optimal behavior. Simulations show that our approach adapts in real time to shifting priorities and achieves up to 80-90\% lower energy consumption and more than 2-5x higher cumulative rewards and packet delivery compared to six baseline protocols, under dynamic and distributed settings. Sensitivity analysis across varying preference window lengths confirms that the proposed DPQ framework consistently achieves higher composite reward than all baseline methods, demonstrating robustness to changes in operating conditions.