We consider gamma-ray burst (GRB) jets that are choked by extended material as sources of high-energy cosmic neutrinos. We take into account the jet propagation physics both inside the progenitor star and the surrounding dense medium. Radiation constraints, which are relevant for high-energy neutrino production are considered as well. Efficient shock acceleration of cosmic rays is possible for sufficiently low-power jets and/or jets buried in a dense, extended wind or outer envelope. Such conditions also favor GRB jets to become stalled, and the necessary conditions for stalling are explicitly derived. Such choked jets may explain transrelativistic supernovae (SNe) and low-luminosity (LL) GRBs, giving a unified picture of GRBs and GRB-SNe. Focusing on this unified scenario for GRBs, we calculate the resulting neutrino spectra from choked jets including the relevant microphysical processes such as multipion production in pp and pγ interactions, as well as the energy losses of mesons and muons. We obtain diffuse neutrino spectra using the latest results for the luminosity function of LL GRBs. Although uncertainties are large, we confirm that LL GRBs can potentially give a significant contribution to the diffuse neutrino flux. Our results are consistent with the present IceCube data and do not violate the stacking limits on classical highluminosity GRBs. We find that high-energy neutrino production in choked jets is dominated by pγ interactions. These sources are dark in GeV-TeV gamma-rays, and do not contribute significantly to the Fermi diffuse gamma-ray background. Assuming stalled jets can launch a quasi-spherical shock in the dense medium, "precursor" TeV neutrinos emerging prior to the shock breakout gamma-ray emission can be used as smoking gun evidence for a choked jet model for LL GRBs. Our results strengthen the relevance of wide field-of-view sky monitors with better sensitivities in the 1−100 keV range.PACS numbers: 95.85. Ry, 97.60.Bw, 98.70.Rz