Millimeter and submillimeter line surveys of the protobinary source IRAS 16293-2422 are presented in the 230 and 345 GHz windows. In total, 265 lines belonging to 44 molecules and their isotopomers (24 chemically different species) have been detected. Here the data for organic and deuterated molecules are considered; the results for Si- and S-bearing species have been discussed in an earlier paper (Blake et al. 1994). The observations have been analyzed through a combination of rotation diagrams and full statistical equilibrium/ radiative transfer calculations. At least three physically and chemically different components can be distinguished within the 20" (3000 AU) beam. The first component is the warm (T_(kin) ≳ 80 K) and dense [^n(H_2) ≍ (0.5-1) × 10^7 cm^(-3)] gas sampled by Si- and S-containing molecules such as SiO and SO_2. This gas is found to be rich in organic molecules such as CH_3OH, CH_3CN, and H_2CO, as well. It is only 3"-10" in size (500-1500 AU) and most likely represents the interaction of the bipolar outflow(s) with the circumbinary envelope. The second component is the circumbinary envelope itself, which has T_(kin) 40 K and n(H_2) 10^6-10^7 cm^(-3) and is 10"-15" in size (2000 AU). It contains common molecules like CS, HCO^+, and H_2CO. The third component is the colder, lower density outer part of the envelope, which gradually fades into the ambient surrounding cloud core [T_(kin) ≍ 10-20 K; n(H_2)≈(3 × 10^4)-(2 × 10^5) cm^(-3)]. Radicals such as CN, C_2H, and C_3H_2 appear to reside principally in this region. The ambient cloud material is also probed through self-absorbed features in the line profiles of molecules such as HCN, HCO^+, and H^2CO. Beam-averaged abundances over a 20" scale are presented and are compared with those observed in cold dark clouds such as L134N and TMC-1 and with high-mass star-forming cores such as Orion-KL. Remarkably high deuterium fractionation ratios are found, which are more characteristic of hot core regions than of cold, quiescent clouds. As a whole, the chemical and physical regimes that can be distinguished in the low-mass young stellar object IRAS 16293-2422 are qualitatively similar to those found in high-mass star-forming regions, confirming the earlier conclusion that the chemical composition depends more on the age of the object than its mass.