We report the implementation of a fully on-chip, lensless, sub-pixel resolving optofluidic microscope (SROFM) based on the super resolution algorithm. 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 red blood cell, microspheres, protist Euglena gracilis, and Entamoeba invadens cysts with sub-cellular resolution. We also demonstrate the capability of SROFM for malaria infected red blood cell diagnostics.