We present infrared (IR) to X-ray spectral energy distributions (SEDs) for 44 red AGN selected from the 2MASS survey on the basis of their red J-K$_S$ color (>2 mag) and later observed by Chandra. In comparison with optically-, radio-, and X-ray selected AGN, their median SEDs are red in the optical and near-IR with little/no blue bump. It thus seems that near-IR color selection isolates the reddest subset of AGN that can be classified optically. The shape of the SEDs is generally consistent with modest absorption by gas (in the X-ray) and dust (in the optical-IR). The levels of obscuration, estimated from X-rays, far-IR and our detailed optical/near-IR color modeling are all consistent implying N_H < few*10^{22} cm^{-2}. We present SED models that show how the AGN optical/near-IR colors change due to differing amounts of reddening, AGN to host galaxy ratio, redshift and scattered light emission and apply them to the sources in the sample. We find that the 2MASS AGN optical color, B-R, and to a lesser extent the near-IR color, J-K$_S$, are strongly affected by reddening, host galaxy emission, redshift, and in few, highly polarized objects, also by scattered AGN light. The obscuration/inclination of the AGN allows us to see weaker emission components which are generally swamped by the AGN.
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