Nonlinear effects in high-speed optical fiber systems fundamentally limit channel capacity. While traditional Digital Backward Propagation (DBP) with adaptive filters addresses these effects, its computational complexity remains impractical. Data-driven solutions like Filtered DBP (FDBP) reduce complexity but critically lack inherent generalization: Their nonlinear compensation capability cannot be naturally extended to new transmission rates or WDM channel counts without retraining on newly collected data. We propose Meta-DSP, a novel signal processing pipeline combining: (1) Meta-DBP, a meta-learning-based DBP model that generalizes across transmission parameters without retraining, and (2) XPM-ADF, a carefully engineered adaptive filter designed to address multi-channel nonlinear distortions. The system demonstrates strong generalization, learning from 40 Gbaud single-channel data and successfully applying this knowledge to higher rates (80/160 Gbaud) and multi-channel configurations (up to 21 channels). Experimental results show Meta-DSP improves Q-factor by 0.55 dB over CDC in challenging scenarios while reducing computational complexity 10$\times$ versus DBP. This work provides a scalable solution for nonlinear compensation in dynamic optical networks, balancing performance with practical computational constraints.