  Fast-spinning strongly magnetized newborn neutron stars, including nascent
magnetars, are popularly implemented as the engine of luminous stellar
explosions. Here, we consider the scenario that they power various
stripped-envelope supernovae, not only super-luminous supernovae Ic but also
broad-line supernovae Ibc and possibly some ordinary supernovae Ibc. This
scenario is also motivated by the hypothesis that Galactic magnetars largely
originate from fast-spinning neutron stars as remnants of stripped-envelope
supernovae. By consistently modeling the energy injection from magnetized wind
and Ni decay, we show that proto-neutron stars with >~ 10 ms rotation and B_dip
>~ 5 x 10^14 G can be harbored in ordinary supernovae Ibc. On the other hand,
millisecond proto-neuton stars can solely power broad-line supernovae Ibc if
they are born with poloidal magnetic field of B_dip >~ 5 x 10^14 G, and
superluminous supernovae Ic with B_dip >~ 10^13 G. Then, we study how
multi-messenger emission can be used to discriminate such pulsar-driven
supernova models from other competitive scenarios. First, high-energy x-ray and
gamma-ray emission from embryonic pulsar wind nebulae is a promising smoking
gun of the underlying newborn pulsar wind. Follow-up observations of
stripped-envelope supernovae using NuSTAR ~ 50-100 days after the explosion is
strongly encouraged for nearby objects. We also discuss possible effects of
gravitational-waves on the spin-down of proto-neutron stars. If millisecond
proto-neutron stars with B_dip <~ a few x 10^13 G emit gravitational waves
through e.g., non-axisymmetric rotation deformed by the inner toroidal fields
of B_t >~ 10^16 G, the gravitational wave signal can be detectable from
ordinary supernova Ibc in the Virgo cluster by Advanced LIGO, Advanced Virgo,
and KAGRA.
