We study the magnetic susceptibility, magnetization, resistivity, and thermal conductivity of intermetallic HoAgGe single crystals at low temperatures and in magnetic fields along the $a$ and $c$ axis, while the electric and heat currents are along the $c$ axis. The magnetization curves show a series of metamagnetic transitions and small hysteresis at low field for $B\ensuremath{\parallel}a$, and a weak metamagnetic transition for $B\ensuremath{\parallel}c$, respectively. Both the magnetic susceptibility and $\ensuremath{\rho}(T)$ curve show anomalies at the antiferromagnetic transition (${T}_{\mathrm{N}}\ensuremath{\sim}11.3$ K) and spin reorientation transition ($\ensuremath{\sim}7$ K). In zero field and at very low temperatures, the electrons are found to be the main heat carriers. For $B\ensuremath{\parallel}a$, the $\ensuremath{\rho}(B)$ curves display large and positive transverse magnetoresistance (MR) with extraordinary field dependence between ${B}^{2}$ and $B$ linear, accompanied with anomalies at the metamagnetic transitions and low-field hysteresis; meanwhile, the $\ensuremath{\kappa}(B)$ mainly decrease with increasing field and display some anomalies at the metamagnetic transitions. For $B\ensuremath{\parallel}c$, there is weak and negative longitudinal MR while the $\ensuremath{\kappa}(B)$ show rather strong field dependence, indicating the role of phonon heat transport.