Multi-path sensing, which aims to extract the geometric attributes of multiple propagation paths, is expected to be a key functionality of 6G. A movable antenna (MA) can enable this functionality by creating a synthetic aperture through sequential mechanical motion. However, existing MA-based sensing methods typically rely on exhaustive scanning over the entire movable plate, resulting in significant control overhead and sensing latency, which limits their practicality for agile sensing. To address this challenge, this paper develops a prior-guided agile multi-path sensing framework that leverages weak prior angle-of-arrival (AoA) statistics as side information. The proposed framework comprises two steps. First, the movable plate's three-dimensional orientation is optimized only once to maximize path visibility while preserving path discriminability, both induced from Fisher information analysis. Second, only two predetermined linear MA scans are made on the tilted plate to estimate the elevation and azimuth AoAs from the resulting sequence of received signals. By incorporating the prior AoA statistics, a maximum a posteriori (MAP)-based AoA estimation algorithm is developed. With only one orientation control and two linear scans, the proposed framework enables agile multi-path sensing with significantly reduced control overhead and latency, while achieving AoA estimation accuracy approaching that of the single-path benchmark.