Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in $\mathrm{<mrow\; data-mjx-texclass="ORD">39</mrow>}$K, as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length $a$ and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the $a4$ scaling of the three-body loss coefficient for both and $a>0$, as well as the many-body loss dynamics at unitarity (where $a$ diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov--van-der-Waals universality in $\mathrm{<mrow\; data-mjx-texclass="ORD">39</mrow>}$K, while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.