We report a multi-epoch, simultaneous 22 GHz H2O and 44 GHz class I CH3OH maser line survey towards 180 intermediate-mass young stellar objects, including 14 Class 0, 19 Class I objects, and 147 Herbig Ae/Be stars. We detected H2O and CH3OH maser emission towards 16 (9%) and 10 (6%) sources with one new H2O and six new CH3OH maser sources. The detection rates of both masers rapidly decrease as the central (proto)stars evolve, which is contrary to the trends in high-mass star-forming regions. This suggests that the excitations of the two masers are closely related to the evolutionary stage of the central (proto)stars and the circumstellar environments. H2O maser velocities deviate on average 9 km s^-1 from the ambient gas velocities whereas CH3OH maser velocities match quite well with the ambient gas velocities. For both maser emissions, large velocity differences (|v_{H2O} - v_{sys} | > 10 km s^-1 and |v_{CH3OH} - v_{sys}| > 1 km s^-1) are mostly confined to Class 0 objects. The formation and disappearance of H2O masers is frequent and their integrated intensities change by up to two orders of magnitude. In contrast, CH3OH maser lines usually show no significant change in intensity, shape, or velocity. This is consistent with the previous suggestion that H2O maser emission originates from the base of an outflow while 44 GHz class I CH3OH maser emission arises from the interaction region of the outflow with the ambient gas. The isotropic maser luminosities are well correlated with the bolometric luminosities of the central objects. The fitted relations are L_{H2O} = 1.71 * 10^{-9} (L_{bol})^{0.97} and L_{CH3OH} = 1.71 * 10^{-10} (L_{bol})^{1.22}.
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