We report the implementation of a fully on-chip, lensless, sub-pixel resolving optofluidic microscope (SROFM). The device utilizes microfluidic flow to deliver specimens directly across a complementary metal oxide semiconductor (CMOS) sensor to generate a sequence of low-resolution (LR) projection images, where resolution is limited by the sensor's pixel size. This image sequence is then processed with a pixel super-resolution algorithm to reconstruct a single high resolution (HR) image, where features beyond the Nyquist rate of the LR images are resolved. We demonstrate the device's capabilities by imaging microspheres, protist Euglena gracilis, and Entamoeba invadens cysts with sub-cellular resolution and establish that our prototype has a resolution limit of 0.75 microns. Furthermore, we also apply the same pixel super-resolution algorithm to reconstruct HR videos in which the dynamic interaction between the fluid and the sample, including the in-plane and out-of-plane rotation of the sample within the flow, can be monitored in high resolution. We believe that the powerful combination of both the pixel super-resolution and optofluidic microscopy techniques within our SROFM is a significant step forwards toward a simple, cost-effective, high throughput and highly compact imaging solution for biomedical and bioscience needs.