  Recent experiments on quantum walks (QWs) of a single and two particles
demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D)
lattices. However the roles of interaction and quantum statistics in such a
kind of walks are little known at a many-body level. In this letter, using
time-evolving block decimation algorithm and many-body perturbation theory we
rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs)
for three indistinguishable bosons and fermions in 1D lattices. We show that
such strongly correlated many-body QWs not only give rise to
statistics-and-interaction-dependent ballistic transports of scattering states,
two- and three-body bound states, but also present a quantum enhanced precision
measurement of the gravitational force. It turns out that in contrast to the
walks of the fermions, the QWs of three bosons exhibit richer dynamics of
co-walkings and competitive Bloch oscillations, which remarkably present a
surprising time scaling $t^3$ of FI below a characteristic time $t_0$ and
saturate to the fundamental limit of $t^2$ for $t>t_0$.
