A quantum dot-like behavior of GaInNAs in Ga0.7In0.3NxAs1-x/GaAs quantum wells (QWs) grown by gas-source molecular-beam epitaxy has been studied using high-resolution x-ray rocking curves (XRC), cross-sectional transmission electron microscopy (XTEM), and photoluminescence (PL) spectroscopy. XRC determines the average alloy composition and thickness of the QWs to be In 0.30 and N 0-0.030, and 6.2 nm, respectively. XTEM images show that the wells of both Ga0.7In0.3As/GaAs and Ga0.7In0.3N0.02As0.98/GaAs are undulated with lateral variations in strain, but the latter is much rougher. For Ga0.7In0.3As/GaAs QWs, rapid thermal annealing results in the splitting of a broad excitonic emission into two peaks presumably due to In composition fluctuation. The separation between these two peaks increases with increasing N concentration. Increasing excitation intensity results in a significant blueshift for the low-energy peak, while little blueshift for the high-energy peak. The earlier PL behavior can be interpreted by a simple model where the low-energy peak originates from In and N-rich regions in the wells acting as quantum dots. The high-energy peak is likely due to the excitons of a more two-dimensional QW.