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This paper presents a responsive strategic oscillation algorithm for the NP-hard disjunctively constrained knapsack problem, which has a variety of applications. The algorithm uses an effective feasible local search to find high-quality local optimal solutions and employs a strategic oscillation search with a responsive filtering strategy to seek still better solutions by searching along the boundary of feasible and infeasible regions. The algorithm additionally relies on a frequency-based perturbation to escape deep local optimal traps. Extensive evaluations on two sets of 6340 benchmark instances show that the algorithm is able to discover 39 new lower bounds and match all the remaining best-known results. Additional experiments are performed on 21 real-world instances of a daily photograph scheduling problem. The critical components of the algorithm are experimentally assessed.