We present results of a long-baseline interferometry campaign using the PAVO beam combiner at the CHARA Array to measure the angular sizes of five main-sequence stars, one subgiant and four red giant stars for which solar-like oscillations have been detected by either Kepler or CoRoT. By combining interferometric angular diameters, Hipparcos parallaxes, asteroseismic densities, bolometric fluxes, and high-resolution spectroscopy, we derive a full set of near-model-independent fundamental properties for the sample. We first use these properties to test asteroseismic scaling relations for the frequency of maximum power (νmax) and the large frequency separation (Δν). We find excellent agreement within the observational uncertainties, and empirically show that simple estimates of asteroseismic radii for main-sequence stars are accurate to <~ 4%. We furthermore find good agreement of our measured effective temperatures with spectroscopic and photometric estimates with mean deviations for stars between T eff = 4600-6200 K of –22 ± 32 K (with a scatter of 97 K) and –58 ± 31 K (with a scatter of 93 K), respectively. Finally, we present a first comparison with evolutionary models, and find differences between observed and theoretical properties for the metal-rich main-sequence star HD 173701. We conclude that the constraints presented in this study will have strong potential for testing stellar model physics, in particular when combined with detailed modeling of individual oscillation frequencies.