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Robust stereo visual-inertial odometry (VIO) remains challenging in low-texture scenes and under abrupt illumination changes, where point features become sparse and unstable, leading to ambiguous association and under-constrained estimation. Line structures offer complementary geometric cues, yet many efficient point-line systems still rely on point-guided line association, which can break down when point support is weak and may lead to biased constraints. We present a stereo point-line VIO system in which line segments are equipped with dedicated deep descriptors and matched using an entropy-regularized optimal transport formulation, enabling globally consistent correspondences under ambiguity, outliers, and partial observations. The proposed descriptor is training-free and is computed by sampling and pooling network feature maps. To improve estimation stability, we analyze the impact of line measurement noise and introduce reliability-adaptive weighting to regulate the influence of line constraints during optimization. Experiments on EuRoC and UMA-VI, together with real-world deployments in low-texture and illumination-challenging environments, demonstrate improved accuracy and robustness over representative baselines while maintaining real-time performance.