  The $\eta$-meson production in photon- and hadron-induced reactions, namely,
$\gamma p \to p \eta$, $\pi^- p \to n \eta$, $pp \to pp\eta$, and $pn \to
pn\eta$, are investigated in a combined analysis in order to learn about the
relevant production mechanisms and the possible role of nucleon resonances in
these reactions. We consider the nucleonic, mesonic, and nucleon resonance
currents constructed within an effective Lagrangian approach and compare the
results with the available data for cross sections and spin asymmetries for
these reactions. We found that the reaction $\gamma p \to p \eta$ could be
described well with the inclusion of the well-established $S_{11}(1535)$,
$S_{11}(1650)$, $D_{13}(1520)$, and $D_{13}(1700)$ resonances, in addition to
the mesonic current. Consideration of other well-established resonances in the
same mass region, including the spin-5/2 resonances, $D_{15}(1675)$ and
$F_{15}(1680)$, does not further improve the results qualitatively. For the
reaction $\pi^- p \to n \eta$, the $P_{13}(1720)$ resonance is found to be
important for reproducing the structure observed in the differential cross
section data. Our model also improves the description of the reaction $NN \to
NN\eta$ to a large extent compared to the earlier results by Nakayama
\textit{et al.} [Phys.\ Rev.\ C \textbf{68}, 045201 (2003)]. For this reaction,
we address two cases where either the $S_{11}(1535)$ or the $D_{13}$ dominates.
Further improvement in the description of these reactions and the difficulty to
uniquely determine the nucleon resonance parameters in the present type of
analysis are discussed.
