We determine all possible equilibrium sequences of compact strange-matter stars with nuclear crusts, which range from massive strange stars to strange white dwarf{endash}like objects (strange dwarfs). The properties of such stars are compared with those of their nonstrange counterparts{emdash}neutron stars and ordinary white dwarfs. The main emphasis of this paper is on strange dwarfs, which we divide into two distinct categories. The first one consists of a core of strange matter enveloped within ordinary white dwarf matter. Such stars are hydrostatically stable with or without the strange core and are therefore referred to as {open_quote}{open_quote}trivial{close_quote}{close_quote} strange dwarfs. This is different for the second category which forms an entirely new class of dwarf stars that contain nuclear material up to 4{times}10{sup 4} times denser than in ordinary white dwarfs of average mass, {ital M}{approximately}0.6 {ital M}{sub {circle_dot}}, and still about 400 times denser than in the densest white dwarfs. The entire family of such dwarfs, denoted {ital dense strange dwarfs}, owes its hydrostatic stability to the strange core. A striking features of strange dwarfs is that the entire sequence from the maximum-mass strange star to the maximum-mass strange dwarf is stable to radial oscillations. The minimum-mass star is only conditionally stable,more » and the sequences on both sides are stable. Such a stable, continuous connection does not exist between ordinary white dwarfs and neutron stars, which are known to be separated by a broad range of unstable stars. We find an expansive range of very low mass (planetary-like) strange-matter stars (masses even below 10{sup {minus}4} {ital M}{sub {circle_dot}} are possible) that arise as natural dark-matter candidates, which if abundant enough in our Galaxy, should be seen in the gravitational microlensing searches that are presently being performed. {copyright} {ital 1995 The American Astronomical Society.}« less