In a crossed molecular beam experiment, the reactive scattering of sodium clusters Na-n (n less than or equal to 33) with molecular oxygen O-2 is investigated. By measuring the angular and the velocity distributions of the scattered reaction products, direct information on the reaction mechanisms is obtained. The sodium clusters are generated in a supersonic expansion of sodium vapor from an oven with a refilling system with argon carrier gas. The products are detected by photoionization at a wavelength of 308 nm and mass analyzed in a time-of-flight mass spectrometer (TOF-MS). In addition, a fast chopper with a pseudorandom sequence modulating the sodium cluster beam allows us to determine at the same time the velocity distributions of the products. The scattering of Na clusters with O-2 shows two series of reaction products. The monoxides NanO are centered around Na3O with 2 less than or equal to n less than or equal to 5, while the metal-rich dioxides NanO2 are detected for 3 less than or equal to n less than or equal to 32 with varying intensities and a maximum at Na5O2. For all products, the measured angular and velocity distributions exhibit forward scattering with a large fraction of the reaction energy deposited into internal excitation of the products. This is in agreement with the classical harpooning model. The general result is explained by the energetic stability of the product complexes.