We observe two secondary eclipses of the strongly irradiated transiting planet WASP-33b, in the Ks band at 2.15 μm, and one secondary eclipse each at 3.6 μm and 4.5 μm using Warm Spitzer. This planet orbits an A5V δ-Scuti star that is known to exhibit low-amplitude non-radial p-mode oscillations at about 0.1% semi-amplitude. We detect stellar oscillations in all of our infrared eclipse data, and also in one night of observations at J band (1.25 μm) out of eclipse. The oscillation amplitude, in all infrared bands except Ks, is about the same as in the optical. However, the stellar oscillations in Ks band (2.15 μm) have about twice the amplitude (0.2%) as seen in the optical, possibly because the Brackett-γ line falls in this bandpass. As regards the exoplanetary eclipse, we use our best-fit values for the eclipse depth, as well as the 0.9 μm eclipse observed by Smith et al., to explore possible states of the exoplanetary atmosphere, based on the method of Madhusudhan & Seager. On this basis we find two possible states for the atmospheric structure of WASP-33b. One possibility is a non-inverted temperature structure in spite of the strong irradiance, but this model requires an enhanced carbon abundance (C/O > 1). The alternative model has solar composition, but an inverted temperature structure. Spectroscopy of the planet at secondary eclipse, using a spectral resolution that can resolve the water vapor band structure, should be able to break the degeneracy between these very different possible states of the exoplanetary atmosphere. However, both of those model atmospheres absorb nearly all of the stellar irradiance with minimal longitudinal re-distribution of energy, strengthening the hypothesis of Cowan & Agol that the most strongly irradiated planets circulate energy poorly. Our measurement of the central phase of the eclipse yields e cos ω = 0.0003 ± 0.00013, which we regard as being consistent with a circular orbit.