Using muon spin rotation, well-defined bulk approximately 100% magnetic phases in NaxCoO2 are revealed. A novel magnetic phase is detected for x=0.85 with the highest transition temperature ever observed for x>or=0.75. This stresses the diversity of x>or=0.75 magnetic phases and the link between magnetic and structural degrees of freedom. For the charge-ordered x=0.50 compound, a cascade of transitions is observed below 85 K. From a detailed analysis of our data, we conclude that the ordered moment varies continuously with temperature and suggest that the two secondary transitions at 48 and 29 K correspond to a moderate reorientation of antiferromagnetically coupled moments.