This study presents the first implementation of multilayer neural networks on a memristor/CMOS integrated system on chip (SoC) to simultaneously detect multiple diseases. To overcome limitations in medical data, generative AI techniques are used to enhance the dataset, improving the classifier's robustness and diversity. The system achieves notable performance with low latency, high accuracy (91.82%), and energy efficiency, facilitated by end-to-end execution on a memristor-based SoC with ten 256x256 crossbar arrays and an integrated on-chip processor. This research showcases the transformative potential of memristive in-memory computing hardware in accelerating machine learning applications for medical diagnostics.