We present images and spectra of the active jet and anomalous arms on subparsec through kiloparsec scales in the LINER/Seyfert galaxy NGC 4258 (M106). New VLBA and multiconfiguration VLA images show that, on 0.3-300 pc scales, the jet in projection aligns with (1) the spin axis of the underlying accretion disk and (2) two radio hot spots 24" S (840 pc) and 49" N (1.7 kpc) from the nucleus. Hubble Space Telescope WFPC2 [N II] λ6583 + Hα images locate interactions between the jet and the interstellar medium (ISM). The most prominent is a pair of emission line arcs whose apices face away from the galaxy nucleus and envelop the leading edges of the radio hot spots. Ground-based (WHT) spectra with 2 Å resolution confirm that the gaseous kinematics and excitation of both arcs have the spatio-kinematic structure expected for jet working surfaces with a shock velocity 350+/-100 km s-1. The north shock is oblique and may lie in a nuclear ionization cone. The south shock shows a detached, putative Mach disk. Models suggest that the S shock is a bow shock around a jet whose progress toward us through the galaxy ISM has stalled. This is notable because the inferred outflow axis is misaligned by ~65° (in three dimensions) with the spin axis of the accretion disk. Our emission line ratios and profiles diagnose the physical properties of the shocks, possible Mach disk, and thence the jets. The shocks lie at one end of a swath of kinematically disturbed gas that reaches back to the previously recognized spiral ``anomalous arms,'' suggesting that they are linked dynamically by precession of the central engine; although claimed elsewhere to be bar shocks, the anomalous arms are probably a fossil record of changing jet activity in NGC 4258. Our results imply that the jet has recently moved a long way out of the plane of the galaxy. A deep Taurus Tunable Filter Hα image shows that discrete strands in the anomalous arms persist to galactocentric radii of at least 4' (>8 kpc), indicating an ongoing ISM interaction. Based on observations made with the NASA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.