We design opportunistic spectrum access strategies for improving spectrum efficiency. In each slot, a secondary user chooses a subset of channels to sense and decides whether to access based on the sensing outcomes. Incorporating the secondary user's residual energy and buffer state, we formulate this sequential decision-making problem as a partially observable Markov decision process (POMDP). Within the POMDP framework, we obtain stationary optimal sensing and access policies. By exploiting the rich structure of the underlying problem, we develop monotonicity results for the optimal policies, which accelerate the computations. Numerical results are provided to study the impact of the secondary user's packet arrival rate and residual energy on the optimal sensing and access decisions.