  We investigate the properties of the ergoregion and the location of the
curvature singularities for the Kerr black hole distorted by the gravitational
field of external sources. The particular cases of quadrupole and octupole
distortion are studied in detail. We also investigate the scalar curvature
invariants of the horizon and compare their behaviour with the case of the
isolated Kerr black hole. In a certain region of the parameter space the
ergoregion consists of a compact region encompassing the horizon and a
disconnected part extending to infinity. The curvature singularities in the
domain of outer communication, when they exist, are always located on the
boundary of the ergoregion. We present arguments that they do not lie on the
compact ergosurface. For quadrupole distortion the compact ergoregion size is
negatively correlated with the horizon angular momentum when the external
sources are varied. For octupole distortion infinitely many ergoregion
configurations can exist for a certain horizon angular momentum. For some
special cases we can have $J^2/M^4 > 1$ and yet avoid the naked singularity.
