  We provide a systematic analysis of the multipolar gravitational waveform,
energy and angular momentum fluxes emitted by a nonspinning test particle
orbiting a Kerr black hole along equatorial, eccentric orbits. These quantities
are computed by numerically solving the Teukolsky equation in the time domain
and are then used to test and improve the radiation reaction (and waveform) of
an effective-one-body (EOB) model. Eccentricity is incorporated into EOB by
replacing the quasi-circular Newtonian (or leading-order) prefactors in the
EOB-factorized multipolar waveform (and fluxes) with their generic
counterparts. The comparison between numerical and analytical quantities is
carried out over a large portion of the parameter space, notably for orbits
close to the separatrix and with high eccentricities. The analytical model
agrees to $\sim 1\%$ with the numerical data for orbits with moderate
eccentricities ($e\lesssim 0.3$) and moderate spins ($\hat{a}\lesssim 0.5$),
although this increases up to $\sim 33\%$ for large, positive, black hole spins
($\sim 0.9$) and large eccentricities ($\sim 0.9$). For moderate
eccentricities, the new EOB fluxes can be used to drive the dynamics through
the nonadiabatic transition from eccentric inspiral to plunge, merger and
ringdown, thus providing accurate an description of the merger. Our approach to
the radiation reaction for eccentric mergers is a first step for computing
accurate waveforms for generic extreme-mass-ratio inspirals. Our EOB model
however can be already applied to study extreme-mass-ratio LISA source.
