We demonstrate submicrotesla sensitivity of organic magnetoresistance in thin-film diodes made of the conducting polymer poly(styrene sulfonate)-doped poly(3,4-ethylenedioxythiophene) (PEDOT:PSS). The magnetoresistance sensitivity is shown to be better than 20 parts per billion (ppb). As for other conjugated polymers, magnetoresistance can be separated into two regimes of field strength: the nonmonotonic ultrasmall magnetic field effect on magnetic field scales below 2 mT, and the monotonic intermediate magnetic field effect on scales over several tens of mT. The former gives the PEDOT:PSS magnetoresistance curve a characteristic W-shaped functionality, with inverted turning points compared to those found in conventional organic light-emitting diode (OLED) devices. We succeed in resolving the ultrasmall magnetic field effect of the PEDOT: PSS layer incorporated within an OLED structure, which is responsible for an additional magnetoresistive feature on the ppm scale. Such a device shows unprecedented complexity in magnetoresistance with a total of four extrema within a field range of +/- 1 mT. We propose that these unique characteristics arise from spin-spin interactions in the weakly bound carrier pairs responsible for the spin-dependent recombination probed in magnetoresistance.