We report dynamic light scattering measurements of the orientational (Frank) elastic constants and associated viscosities among a homologous series of a liquid crystalline dimer, trimer, and tetramer exhibiting a uniaxial nematic (N) to twist-bend nematic (N ) phase transition. The elastic constants for director splay (K ), twist (K ) and bend (K ) exhibit the relations K > K > K and K /K > 2 over the bulk of the N phase. Their behavior near the N-N transition shows dependency on the parity of the number (n) of the rigid mesomorphic units in the flexible n-mers. Namely, the bend constant K in the dimer and tetramer turns upward and starts increasing close to the transition, following a monotonic decrease through most of the N phases. In contrast, K for the trimer flattens off just above the transition and shows no pretransitional enhancement. The twist constant K increases pretransitionally in both even and odd n-mers, but more weakly so in the trimer, while K increases steadily on cooling without evidence of pretransitional behavior in any n-mer. The viscosities associated with pure splay, twist-dominated twist-bend, and pure bend fluctuations in the N phase are comparable in magnitude to those of rod-like monomers. All three viscosities increase with decreasing temperature, but the bend viscosity in particular grows sharply near the N-N transition. The N-N pretransitional behavior is shown to be in qualitative agreement with the predictions of a coarse-grained theory, which models the N phase as a "pseudo-layered" structure with the symmetry (but not the mass density wave) of a smectic-A* phase.