Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N<or=20 and X=F, Cl, Br. The calculations are done using ab initio He-HX intermolecular potentials whose computation is described. Intermolecular energies and He radial and angular probability density distributions are computed as a function of the number of solvent atoms. Excited states are calculated using fixed-node diffusion Monte Carlo methods, and molecule-solvent angular momentum coupling is studied as a function of cluster size and potential anisotropy. Nodal surfaces of the many-body wave function are computed approximately by making an adiabatic Born-Oppenheimer-like separation of radial and angular degrees of freedom of the cluster. This procedure is extended to include radial dependencies in the adiabatic nodal function. We predict that the observed decrease in the gas-phase rotational constants for HCl and HBr in a 4He nanodroplet will be smaller than that observed for HF, despite HF's having the largest (by far) gas-phase rotational constant of the three molecules. This suggests that the specifics of the solvation dynamics of a molecule in a 4He cluster are the result of a delicate interplay between the magnitude of the gas-phase rotational constant of the molecule and the anisotropic contributions to the atom-molecule potential energy.