Rapid and accurate building damage assessment in the immediate aftermath of tornadoes is critical for coordinating life-saving search and rescue operations, optimizing emergency resource allocation, and accelerating community recovery. However, current automated methods struggle with the unique visual complexity of tornado-induced wreckage, primarily due to severe domain shift from standard pre-training datasets and extreme class imbalance in real-world disaster data. To address these challenges, we introduce a systematic experimental framework evaluating 79 open-source deep learning models, encompassing both Convolutional Neural Networks (CNNs) and Vision Transformers, across over 2,300 controlled experiments on our newly curated Quad-State Tornado Damage (QSTD) benchmark dataset. Our findings reveal that achieving operational-grade performance hinges on a complex interaction between architecture and optimization, rather than architectural selection alone. Most strikingly, we demonstrate that optimizer choice can be more consequential than architecture: switching from Adam to SGD provided dramatic F1 gains of +25 to +38 points for Vision Transformer and Swin Transformer families, fundamentally reversing their ranking from bottom-tier to competitive with top-performing CNNs. Furthermore, a low learning rate of 1x10^(-4) proved universally critical, boosting average F1 performance by +10.2 points across all architectures. Our champion model, ConvNeXt-Base trained with these optimized settings, demonstrated strong cross-event generalization on the held-out Tuscaloosa-Moore Tornado Damage (TMTD) dataset, achieving 46.4% Macro F1 (+34.6 points over baseline) and retaining 85.5% Ordinal Top-1 Accuracy despite temporal and sensor domain shifts.