We present a detailed study of the energetics, structures, and Bose properties of small clusters of He-4 containing a single nitrous oxide (N2O) molecule, from N=1 He-4 up to sizes corresponding to completion of the first solvation shell around N2O (N=16 He-4). Ground state properties are calculated using the importance-sampled rigid-body diffusion Monte Carlo method, rotational excited state calculations are made with the projection operator imaginary time spectral evolution method, and Bose permutation exchange and associated superfluid properties are calculated with the finite temperature path integral method. For Nless than or equal to5 the helium atoms are seen to form an equatorial ring around the molecular axis, at N=6 helium density starts to occupy the second (local) minimum of the N2O-He interaction at the oxygen side of the molecule, and N=9 is the critical size at which there is onset of helium solvation all along the molecular axis. For Ngreater than or equal to8 six He-4 atoms are distributed in a symmetric, quasirigid ring around N2O. Path integral calculations show essentially complete superfluid response to rotation about the molecular axis for Ngreater than or equal to5, and a rise of the perpendicular superfluid response from zero to appreciable values for Ngreater than or equal to8. Rotational excited states are computed for three values of the total angular momentum, J=1-3, and the energy levels fitted to obtain effective spectroscopic constants that show excellent agreement with the experimentally observed N dependence of the effective rotational constant B-eff. The non-monotonic behavior of the rotational constant is seen to be due to the onset of long He-4 permutation exchanges and associated perpendicular superfluid response of the clusters for Ngreater than or equal to8. We provide a detailed analysis of the role of the helium solvation structure and superfluid properties in determining the effective rotational constants. (C) 2004 American Institute of Physics.