Learning-based lossless compressors play a crucial role in large-scale genomic database backup, storage, transmission, and management. However, their 1) inadequate compression ratio, 2) low compression \& decompression throughput, and 3) poor compression robustness limit their widespread adoption and application in both industry and academia. To solve those challenges, we propose a novel \underline{P}arallel \underline{M}ulti-\underline{K}nowledge \underline{L}earning-based \underline{C}ompressor (PMKLC) with four crucial designs: 1) We propose an automated multi-knowledge learning-based compression framework as compressors' backbone to enhance compression ratio and robustness; 2) we design a GPU-accelerated ($s$,$k$)-mer encoder to optimize compression throughput and computing resource usage; 3) we introduce data block partitioning and Step-wise Model Passing (SMP) mechanisms for parallel acceleration; 4) We design two compression modes PMKLC-S and PMKLC-M to meet the complex application scenarios, where the former runs on a resource-constrained single GPU and the latter is multi-GPU accelerated. We benchmark PMKLC-S/M and 14 baselines (7 traditional and 7 leaning-based) on 15 real-world datasets with different species and data sizes. Compared to baselines on the testing datasets, PMKLC-S/M achieve the average compression ratio improvement up to 73.609\% and 73.480\%, the average throughput improvement up to 3.036$\times$ and 10.710$\times$, respectively. Besides, PMKLC-S/M also achieve the best robustness and competitive memory cost, indicating its greater stability against datasets with different probability distribution perturbations, and its strong ability to run on memory-constrained devices.