In external galaxies, molecular composition may be influenced by extreme environments such as starbursts and galaxy mergers. To study such molecular chemistry, we observed the luminous infrared galaxy and merger NGC 3256 using the Atacama Large Millimeter/submillimeter Array. We covered most of the 3 and 1.3mm bands for a multispecies, multitransition analysis. We first analyzed intensity ratio maps of selected lines such as HCN/HCO^+^, which shows no enhancement at an active galactic nucleus. We then compared the chemical compositions within NGC 3256 at the two nuclei, tidal arms, and positions with influence from galactic outflows. We found the largest variation in SiO and CH_3_OH, species that are likely to be enhanced by shocks. Next, we compared the chemical compositions in the nuclei of NGC 3256, NGC 253, and Arp 220; these galactic nuclei have varying star formation efficiencies. Arp 220 shows higher abundances of SiO and HC_3_N than NGC 3256 and NGC 253. Abundances of most species do not show a strong correlation with star formation efficiencies, although the CH_3_CCH abundance seems to have a weak positive correlation with the star formation efficiency. Lastly, the chemistry of spiral arm positions in NGC 3256 is compared with that of W51, a Galactic molecular cloud complex in a spiral arm. We found higher fractional abundances of shock tracers, and possibly also a higher dense gas fraction in NGC 3256 compared with W51.