  The magnetic properties of a pressure induced noncentrosymmetric
heavy-fermion superconductor CeIrGe$_3$ have been investigated by muon spin
relaxation ($\mu$SR), powder neutron diffraction (ND) and inelastic neutron
scattering (INS) techniques at ambient pressure. For completeness we have also
measured the ac magnetic susceptibility $\chi_{\rm ac}(T)$, dc magnetic
susceptibility $\chi(T)$, dc isothermal magnetization $M(H)$ and heat capacity
$C_{\rm p}(T,H)$ down to 2 K. CeIrGe$_{3}$ is known to exhibit pressure induced
superconductivity ($T_{\rm c}\approx 1.5$ K) at a pressure of 20 GPa and
antiferromagnetic ordering at 8.7 K, 4.7 K and 0.7 K at ambient pressure. Our
$\chi_{\rm ac}(T)$ and $\chi(T)$ data show an additional anomaly near 6.2 K
which is also captured in $C_{\rm p}(T)$ data. From $\chi_{\rm ac}(T)$,
$\chi(T)$ and $C_{\rm p}(T)$ measurements we infer three antiferromagnetic
transitions above 2 K at $T_{\rm N1}= 8.5$ K, $T_{\rm N2}= 6.0$ K and $T_{\rm
N3}= 4.6$ K. Our $\mu$SR study also confirms the presence of three transitions
through the observation of one frequency for $T_{\rm N2} < T\leq T_{\rm N1}$,
two frequencies for $T_{\rm N3} < T\leq T_{\rm N2}$ and three frequencies for
$T\leq T_{\rm N3}$ in the oscillatory asymmetry. The ND data reveal an
incommensurate nature of the magnetic ordering at $T=7$ K with the propagation
vector k = (0,0,0.688(3)), and a commensurate magnetic structure at $T=1.5$ K
with the propagation vector locked to the value k = (0,0,2/3) and magnetic
moments oriented along the $c$ axis. The commensurate structure couples a
macroscopic ferromagnetic component, resulting in a strong dependence of the
lock-in transition temperature on external magnetic field. The INS data show
two well defined crystal electric field (CEF) excitations arising from the
CEF-split Kramers doublet ground state of Ce$^{3+}$.
