Positions, intensities, self-broadened widths, and collisional narrowing coefficients of the oxygen isotopologues (OO)-O-16-O-18, (OO)-O-16-O-17, (OO)-O-17-O-18, and (OO)-O-18-O-18 have been measured for the b(1)Sigma(g) + <-- X-3 Sigma g - (0,0) band using frequency-stabilized cavity ring-down spectroscopy. Line positions of 156 P-branch transitions were referenced against the hyperfine components of the K-39 D-1 (4s 2S(1/2) --> 4p P-2(1/2)) and D-2 (4s S-2(1/2) --> 4P P-2(3/2)) transitions, yielding precisions of similar to 0.00005 cm(-1) and absolute accuracies of 0.00030 cm(-1) or better. New excited b(1)Sigma g + state molecular constants are reported for all four isotopologues. The measured line intensities of the (OO)-O-16-O-18 isotopologue are within 2% of the values currently assumed in molecular databases. However, the line intensities of the (OO)-O-16-O-17 isotopologue show a systematic, J-dependent offset between our results and the databases. Self-broadening half-widths for the various isotopologues are internally consistent to within 2%. This is the first comprehensive Study of the line intensities and shapes for the (OO)-O-17-O-18 or O-18(2) isotopologues of the b(1)Sigma g + <--X-3 Sigma g - (0,0) band of O-2. The O-16(2), (OO)-O-16-O-18, and (OO)-O-16-O-17 line parameters for the oxygen A-band have been extensively revised in the HITRAN 2008 database using results from the present study.