Dense molecular gas tracers in the central 1 kpc region of the superwind galaxy NGC 1808 have been imaged by ALMA at a resolution of 1″ (∼50 pc). Integrated intensities and line intensity ratios of HCN (1-0), H13CN (1-0), HCO+ (1-0), H13CO+ (1-0), HOC+ (1-0), HCO+ (4-3), CS (2-1), C2H (1-0), and previously detected CO (1-0) and CO (3-2) are presented. SiO (2-1) and HNCO (4-3) are detected toward the circumnuclear disk (CND), indicating the presence of shocked dense gas. There is evidence that an enhanced intensity ratio of HCN (1-0)/HCO+ (1-0) reflects star formation activity, possibly in terms of shock heating and electron excitation in the CND and a star-forming ring at radius ∼300 pc. A non-local thermodynamic equilibrium analysis indicates that the molecular gas traced by HCN, H13CN, HCO+, and H13CO+ in the CND is dense ( ) and warm (20 K Tk 100 K). The calculations yield a low average gas density of for a temperature of in the nuclear outflow. Dense gas tracers HCN (1-0), HCO+ (1-0), CS (2-1), and C2H (1-0) are detected for the first time in the superwind of NGC 1808, confirming the presence of a velocity gradient in the outflow direction.