$\theta$-TaN is a promising ultrahigh thermal conductivity material, yet a notable discrepancy remains between previous molecular dynamics (MD) simulations and experiments. A systematic atomistic understanding of how directional thermal transport is modulated by synthesis-induced point defects and tensile strain is also lacking. Here, we develop a Neuroevolution Potential (NEP) trained on and evaluated against density-functional-theory (DFT) data to investigate the lattice thermal conductivity (${\kappa }_L$) of $\theta$-TaN. By applying a noise extrapolation method to mitigate artificial phonon scattering from errors in force fitting, the pristine ${\kappa }_L$ extrapolated to zero force noise reduces the discrepancy with experiments and Boltzmann transport equation (BTE) predictions, supporting finite force errors as one contributor to the underestimation in previous MD results. On this basis, the effects of four representative point defects—${\mathrm{\text{V}}}_{\mathrm{\text{N}}}$, ${\mathrm{\text{V}}}_{\mathrm{\text{Ta}}}$, ${\mathrm{\text{N}}}_{\mathrm{\text{Ta}}}$, and ${\mathrm{\text{N}}}_i$—are evaluated across concentrations from $2.31\times {10}^{18}$ to $44.4\times {10}^{18}{cm}^{-3}$. Among the considered defects, $N_{Ta}$ gives the lowest sampled mean ${\kappa }_L$ at the evaluated concentration limits, accompanied by pronounced perturbations of modes at low frequencies and a high frequency vibrational feature induced by the defect. Additionally, equiaxial tensile strain ($\epsilon =0$ to 0.06) monotonically suppresses ${\kappa }_L$ by over one order of magnitude. The consistent trends in the spectral thermal conductivities obtained from MD and the phonon properties derived from three-phonon calculations indicate that bond weakening, phonon softening, reduced phonon group velocities, and shorter relaxation times contribute to the strain-induced reduction in ${\kappa }_L$. This work illustrates the utility of the noise extrapolation method in mitigating artifacts caused by force noise in MD simulations and provides insight into the defect- and strain-modulated thermal transport in $\theta$-TaN.