Deep learning has revolutionized oncology by enabling unprecedented integration of multimodal data for cancer diagnosis and prognosis. This comprehensive survey presents the first systematic analysis of deep learning architectures across four major cancer types (lung, breast, skin, and brain) through three critical data modalities: medical imaging, histopathology, and genomics. Our unique contribution lies in providing a structured taxonomy of multimodal fusion strategies and identifying critical architectural innovations that have emerged in the 2021–2025 period. We systematically analyze 60+ recent studies, revealing that attention-based mechanisms and Transformer architectures demonstrate superior performance in handling heterogeneous cancer data compared to traditional CNN approaches. Our analysis uncovers three key research gaps: (1) limited interpretability frameworks for clinical deployment, (2) insufficient standardization across institutions, and (3) scalability challenges for real-world implementation. This survey uniquely bridges the gap between theoretical deep learning advances and practical oncological applications by proposing a unified framework for multimodal cancer analysis. We provide actionable insights for researchers and clinicians, establishing clear directions for future development in AI-driven cancer care that addresses both technical innovation and clinical translation requirements.