We have conducted a survey of C3H2, HC3N, and C2S (two rotational transitions in each) in our standard sample of 11 cirrus cores and 27 Clemens-Barvainis translucent cores whose structures and chemistry have been studied in this series. C3H2 is seen in 31 objects, HC3N in six, and C2S in 14. These results are modeled in terms of our previous hydrostatic equilibrium and n ~ r-α structures together with other chemical and physical properties derived earlier. The complex radiative transfer and excitation of C3H2 and HC3N is discussed, including weak population inversions in the lower states. Radiative transfer of C2S is less complicated. Abundances of each species increase monotonically with increasing extinction in the 1.2-2.7 mag range (edge-to-center), thus displaying the same characteristic transition between diffuse and dense cloud chemistry as do most other species we have studied. The chemistry has been modeled by solving the complete set of ~4000 reactions in the New Standard Chemistry Model, adapted to translucent cloud conditions of density, elemental abundances, extinctions, and certain ion-polar rates. C3H2 abundances are underestimated by the Standard chemistry model by a factor of ~10, resulting, we believe, from a single uncertain reaction rate and perhaps one omitted neutral-neutral process. HC3N and C2S abundances fit chemistry model predictions well. They appear not to be intimately connected chemically with C3H2. Aside from the overall success of the gas-phase chemistry models, we emphasize that (1) the observed abundances are consistent with steady state chemistry, not early-time chemistry, and (2) neutral-neutral reactions are fundamentally important in forming HC3N, possibly important to C3H2, and not important to C2S.