  We present $29\pm1$ classical Oe stars from RIOTS4, a spatially complete,
spectroscopic survey of Small Magellanic Cloud (SMC) field OB stars. The two
earliest are O6e stars, and four are earlier than any Milky Way (MW) Oe stars.
We also find ten Ope stars, showing He~\textsc{i} infill and/or emission; five
appear to be at least as hot as $\sim$O7.5e stars. The hottest, star 77616,
shows He~\textsc{ii} disk emission, suggesting that even the hottest O stars
can form decretion disks, and offers observational support for theoretical
predictions that the hottest, fastest rotators can generate He$^+$-ionizing
atmospheres. Our data also demonstrate that Ope stars correspond to Oe stars
earlier than O7.5e with strong disk emission. We find that in the SMC, Oe stars
extend to earlier spectral types than in the MW, and our SMC Oe/O frequency,
$0.26\pm0.04$, is much greater than the MW value, $0.03\pm0.01$. These results
are consistent with angular momentum transport by stronger winds suppressing
decretion disk formation at higher metallicity. In addition, our SMC field Oe
star frequency is indistinguishable from that for clusters, which is consistent
with the similarity between rotation rates in these environments, and contrary
to the pattern for MW rotation rates. Thus, our findings strongly support the
viscous decretion disk model and confirm that Oe stars are the high-mass
extension of the Be phenomenon. Additionally, we find that Fe~\textsc{ii}
emission occurs among Oe stars later than O7.5e with massive disks, and we
revise a photometric criterion for identifying Oe stars to $J-[3.6] \geq 0.1$.
