Using the BaLROG (Bars in Low Redshift Optical Galaxies) sample of 16 morphologically distinct barred spirals, we constrain the influence of bars on nearby galaxies observationally. Our sample appears small compared to ongoing IFU surveys, but offers a tenfold sharper spatial resolution (˜100 pc) as each galaxy is a mosaic of several pointings observed with the IFU spectrograph SAURON. We demonstrate a correlation between the bar strength Qb determined from classical torque analysis using 3.6 μm Spitzer (S4G) images, with Qkin, a kinematic torque, calculated via our new method based solely on the kinematics. Using a large number of N-body simulations, we verify this correlation and the measurement of Qb. We also determine bar strengths from ionized gas kinematics and find that they are ˜2.5 larger than those measured from stellar kinematics. Further, inner kinematic features related to bars as predicted by simulations seem to be stronger for stronger bars. We find a stellar angular momentum dip at 0.2±0.1 bar lengths. In these central regions, about half of our sample also exhibits an anti-correlation of h3 - stellar velocity (v/σ). An increased flattening of the stellar σ gradient with increasing bar strength supports the notion of bar-induced orbit mixing. Our results constrain the spatial scales and magnitude of a kinematic influence of bar-driven secular evolution in present day galaxies.