Out-of-town trip recommendation aims to generate a sequence of Points of Interest (POIs) for users traveling from their hometowns to previously unvisited regions based on personalized itineraries, e.g., origin, destination, and trip duration. Modeling the complex user preferences--which often exhibit a two-fold nature of static and dynamic interests--is critical for effective recommendations. However, the sparsity of out-of-town check-in data presents significant challenges in capturing such user preferences. Meanwhile, existing methods often conflate the static and dynamic preferences, resulting in suboptimal performance. In this paper, we for the first time systematically study the problem of out-of-town trip recommendation. A novel framework SPOT-Trip is proposed to explicitly learns the dual static-dynamic user preferences. Specifically, to handle scarce data, we construct a POI attribute knowledge graph to enrich the semantic modeling of users' hometown and out-of-town check-ins, enabling the static preference modeling through attribute relation-aware aggregation. Then, we employ neural ordinary differential equations (ODEs) to capture the continuous evolution of latent dynamic user preferences and innovatively combine a temporal point process to describe the instantaneous probability of each preference behavior. Further, a static-dynamic fusion module is proposed to merge the learned static and dynamic user preferences. Extensive experiments on real data offer insight into the effectiveness of the proposed solutions, showing that SPOT-Trip achieves performance improvement by up to 17.01%.