Red giants with solar-like oscillations are astrophysical laboratories for probing the Milky Way. The Kepler Space Telescope revolutionized asteroseismology by consistently monitoring thousands of targets, including several red giants in eclipsing binaries. Binarity allows us to directly measure stellar properties independently of asteroseismology. In this dissertation, we study a subset of eight red giant eclipsing binaries observed by Kepler with a range of orbital periods, oscillation behavior, and stellar activity. Two of the systems do not show solar-like oscillations at all. We use a suite of modeling tools to combine photometry and spectroscopy into a comprehensive picture of each star's life. One noteworthy case is a double red giant binary. The two stars are nearly twins, but have one main set of solar-like oscillations with unusually low-amplitude, wide modes, likely due to stellar activity and modest tidal forces acting over the 171 day eccentric orbit. Mixed modes indicate the main oscillating star is on the secondary red clump (a core-He-burning star), and stellar evolution modeling supports this with a coeval history for a pair of red clump stars. The other seven systems are all red giant branch stars (shell-H-burning) with main sequence companions. The two non-oscillators have the strongest magnetic signatures and some of the strongest lifetime tidal forces with nearly-circular 20-34 day orbits. One system defies this trend with oscillations and a 19 day orbit. The four long-period systems (>100 days) have oscillations, more eccentric orbits, and less stellar activity. They are all detached binaries consistent with coevolution. We find the asteroseismic scaling laws are approximately correct, but fail the most for stars that are least like the Sun by systematically overestimating both mass and radius. Strong magnetic activity and tidal effects often occur in tandem and act to suppress solar-like oscillations. These red giant binaries offer an unprecedented opportunity to test stellar physics and are important benchmarks for ensemble asteroseismology. Future asteroseismic studies should know they are excluding magnetically active stars and close binaries and be aware that asteroseismic masses and radii are both overestimated.