  We present Herschel-HIFI, SPIRE, and PACS 50-670 {\mu}m imaging and
spectroscopy of six FU Orionis-type objects and candidates (FU Orionis, V1735
Cyg, V1515 Cyg, V1057 Cyg, V1331 Cyg, and HBC 722), ranging in outburst date
from 1936-2010, from the "FOOSH" (FU Orionis Objects Surveyed with Herschel)
program, as well as ancillary results from Spitzer-IRS and the Caltech
Submillimeter Observatory. In their system properties (Lbol, Tbol, line
emission), we find that FUors are in a variety of evolutionary states.
Additionally, some FUors have features of both Class I and II sources: warm
continuum consistent with Class II sources, but rotational line emission
typical of Class I, far higher than Class II sources of similar
mass/luminosity. Combining several classification techniques, we find an
evolutionary sequence consistent with previous mid-IR indicators. We detect [O
I] in every source at luminosities consistent with Class 0/I protostars, much
greater than in Class II disks. We detect transitions of 13CO (J_up of 5 to 8)
around two sources (V1735 Cyg and HBC 722) but attribute them to nearby
protostars. Of the remaining sources, three (FU Ori, V1515 Cyg, and V1331 Cyg)
exhibit only low-lying CO, but one (V1057 Cyg) shows CO up to J = 23 - 22 and
evidence for H2O and OH emission, at strengths typical of protostars rather
than T Tauri stars. Rotational temperatures for "cool" CO components range from
20-81 K, for ~ 10^50 total CO molecules. We detect [C I] and [N II] primarily
as diffuse emission.
