  (Abridged) We present new, deep HI line and 20-cm radio continuum data of the
very puzzling blue compact dwarf galaxy NGC 5253, obtained with the ATCA as
part of the `Local Volume HI Survey' (LVHIS). Our low-resolution HI maps show
the disturbed HI morphology that NGC 5253 possesses, including tails, plumes
and detached HI clouds. The high-resolution map reveals an HI plume at the SE
and an HI structure at the NW that surrounds an Ha shell. We confirm that the
kinematics of the neutral gas are highly perturbed and do not follow a rotation
pattern. We discuss the outflow and infall scenarios to explain such disturbed
kinematics, analyze the environment in which it resides, and compare it
properties with those observed in similar star-forming dwarf galaxies. The
radio-continuum emission of NGC 5253 is resolved and associated with the
intense star-forming region at the center of the galaxy. We complete the
analysis using multiwavelength data extracted from the literature. We estimate
the SFR using this multiwavelength approach. NGC 5253 does not satisfy the
Schmidt-Kennicutt law of star-formation, has a very low HI mass-to-light ratio
when comparing with its stellar mass, and seems to be slightly metal-deficient
in comparison with starbursts of similar baryonic mass. Taking into account all
available multiwavelength data, we conclude that NGC 5253 is probably
experiencing the infall of a diffuse, low-metallicity HI cloud along the minor
axis of the galaxy, which is comprising the ISM and triggering the powerful
starburst. The tidally disturbed material observed at the east and north of the
galaxy is a consequence of this interaction, which probably started more than
100 Myr ago. The origin of this HI cloud may be related with a strong
interaction between NGC 5253 and the late-type spiral galaxy M 83 in the past.
