We investigate the use of mid-infrared (MIR) polycyclic aromatic hydrocarbon (PAH) bands, the continuum, and emission lines as probes of star formation (SF) and active galactic nucleus (AGN) activity in a sample of 100 "normal" and local (z ~ 0.1) emission-line galaxies. The MIR spectra were obtained with the Spitzer Space Telescope Infrared Spectrograph as part of the Spitzer-SDSS-GALEX Spectroscopic Survey, which includes multi-wavelength photometry from the ultraviolet to the far-infrared and optical spectroscopy. The continuum and features were extracted using PAHFIT, a decomposition code which we find to yield PAH equivalent widths (EWs) up to ~30 times larger than the commonly used spline methods. Despite the lack of extreme objects in our sample (such as strong AGNs, low-metallicity galaxies, or ULIRGs), we find significant variations in PAH, continuum, and emission-line properties, and systematic trends between these MIR properties and optically derived physical properties, such as age, metallicity, and radiation field hardness. We revisit the diagnostic diagram relating PAH EWs and [Ne II]12.8 μm/[O IV]25.9 μm line ratios and find it to be in much better agreement with the standard optical SF/AGN classification than when spline decompositions are used, while also potentially revealing obscured AGNs. The luminosity of individual PAH components, of the continuum, and, with poorer statistics, of the neon emission lines and molecular hydrogen lines are found to be tightly correlated to the total infrared (TIR) luminosity, making individual MIR components good gauges of the total dust emission in SF galaxies. Like the TIR luminosity, these individual components can be used to estimate dust attenuation in the UV and in Hα lines based on energy balance arguments. We also propose average scaling relations between these components and dust-corrected, Hα-derived SF rates.