We report ALMA and SMA observations of the luminous infrared merger NGC 3256, the most luminous galaxy within z=0.01. Both of the two merger nuclei separated by 5 (0.8 kpc) on the sky have a compact concentration of molecular gas, i.e., nuclear disks with Sigma_mol > 10^3 Msun pc^-2. The one at the northern nucleus is face-on while the southern nuclear disk is almost edge-on. The northern nucleus is more massive and has molecular arcs and spiral arms around. The high-velocity molecular gas previously found in the system is resolved to two molecular outflows associated with each of the two nuclei. The molecular outflow from the northern nuclear disk is part of a starburst-driven superwind seen nearly pole on. Its maximum velocity is >750 km/s and its mass outflow rate is estimated to be > 60 Msun/yr for a conversion factor N_{H_2}/I_{CO(1-0)}=1x10^20 cm^-2/(K km/s). The outflow from the southern nucleus is a highly collimated bipolar molecular jet seen nearly edge-on. Its line-of-sight velocity increases with distance out to 300 pc from the southern nucleus. Its maximum de-projected velocity is ~2000 km/s for the estimated inclination and should exceed 1000 km/s even allowing for its uncertainty. The mass outflow rate is estimated to be >50 Msun/yr for this outflow. There are possible signs that this southern outflow has been driven by a bipolar radio jet from an AGN that became inactive very recently. The sum of these outflow rates, although subject to the uncertainty in the molecular mass estimate, either exceeds or compares to the total star formation rate in NGC 3256. The feedback from nuclear activities in the form of molecular outflows is therefore significant in the gas consumption budget, and hence evolution, of this luminous infrared galaxy. (abridged)
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