We use Fabry-Perot and long-slit spectra with radio, molecular, and X-ray data sets to study the twisted, multistrand jets in the nearby active galaxy NGC 4258 (M106). Their several arcminute extent and the extensive wavelength coverage of their interaction with the ISM make these jets an important laboratory for studying the processes likely to dominate the appearance of high-z radio galaxies. A VLA A-array image at 20 cm traces the jet down to 2 '' (70 pc) radius and shows that it is perpendicular to the subparsec nuclear disk that is delineated by H2O masers. Our long-slit spectra span the jet and range over 3640-8560 Angstrom at 4.5 Angstrom resolution. We measure a central stellar velocity dispersion of 171 km s(-1). This is smaller than the line widths of the ionized gas and is too low to explain the observed oscillations in the centroids of the emission-line profiles by virial motion within the bulge potential. Mean stellar velocities agree with those of the gas along the jet axis and are consistent with bar-forced motions in the large-scale disk of the galaxy. From the emission-line flux ratios, we find LINER-like gaseous excitation along the jets and constrain the gas temperatures. For the N+ and O+ emitting gas, we found that T < 10(4) K, and for the S+ gas T < 19,000 K. The O++ temperature is weakly constrained to be less than 30,000 K. Flux ratios remain constant along the SE jet, with ionization parameter log U approximate to -3.5, Our models show that these ratios can be generated by approximate to 350 km s(-1) shocks velocities consistent with the amplitude of kinematic oscillations in the emission-line profiles and with the observed thermal X-ray spectrum of the jet of temperature 0.3 keV. A modest ambient gas density of 0.2 cm(-3) can produce both the jet's X-ray flux and enough ionizing photons to account for the jet's H alpha flux. In contrast, the present ionizing flux from the AGN is approximate to 10(3) times too low to directly photoionize the jets. Therefore, molecular gas that is known to lie along the jets may be shocked and photoionized locally as it is entrained. We constrain the star formation induced by the SE jet. The jets do not emit a continuum within the interval lambda lambda = 0.38-0.88 mu m down to a surface brightness of 3 x 10(-17) ergs cm(-2) s(-1) Angstrom(-1) arcsec(-2).