Alzheimer's Disease (AD) represents a growing global health crisis characterized by progressive cognitive decline, memory impairment, and irreversible brain atrophy. The heterogeneous and irregular nature of longitudinal clinical data presents significant challenges for accurate disease progression modeling, with existing methods struggling with irregular sampling, effective multimodal integration, and simultaneous prediction of multiple clinical outcomes. To address these limitations, we propose an enhanced Neural Ordinary Differential Equations (Neural ODEs) framework that leverages continuous-time dynamics with fourth-order Runge-Kutta (RK4) integration to model AD progression from irregular longitudinal observations. Our approach incorporates a dual-attention multimodal fusion mechanism for task-specific feature weighting and an adaptive multi-task learning strategy with dynamic task balancing. Evaluated on the OASIS-2 dataset, a comprehensive ablation study across six modality-task configurations shows that our multimodal multi-task framework achieves the best overall performance, with the complete model obtaining a mean diagnosis AUC of 0.842, accuracy of 0.744, MMSE R‑squared of 0.575, CDR R‑squared of 0.138, and atrophy R‑squared of 0.510. Our framework outperforms single-modality baselines with robust convergence and interpretable features, advancing integrated AD progression modeling.