We present a Far-Ultraviolet Spectroscopic Explorer survey of highly ionized high-velocity clouds ( HVCs ) in 66 extragalactic sight lines with S/N _ { 1030 } > 8 . We searched the spectra for high-velocity ( 100 < |v _ { LSR } | < 400 km s ^ { -1 } ) O vi absorption and found a total of 63 absorbers , 16 with 21 cm-emitting H i counterparts and 47 “ highly ionized ” absorbers without 21 cm emission . The highly ionized HVC population is characterized by \langle b ( O vi ) \rangle =38 \pm 10 km s ^ { -1 } and \langle log N _ { a } ( O vi ) \rangle =13.83 \pm 0.36 , with negative-velocity clouds generally found at l < 180 ° and positive-velocity clouds found at l > 180 ° . 11 of these high-velocity O vi absorbers are positive-velocity wings ( broad O vi features extending asymmetrically to velocities of up to 300 km s ^ { -1 } ) . We find that 81 % ( 30/37 ) of high-velocity O vi absorbers have clear accompanying C iii absorption , and 76 % ( 29/38 ) have accompanying H i absorption in the Lyman series . We present the first ( O vi-selected ) sample of C iii and H i absorption line HVCs , and find \langle b ( C iii ) \rangle =30 \pm 8 km s ^ { -1 } , log N _ { a } ( C iii ) ranges from 12.8 to > 14.4 , \langle b ( H i ) \rangle =22 \pm 5 km s ^ { -1 } , and log N _ { a } ( H i ) ranges from 15.1 to > 16.9 . The lower average width of the high-velocity H i absorbers implies the H i lines arise in a separate , lower temperature phase than the O vi . The ratio N _ { a } ( C iii ) / N _ { a } ( O vi ) is generally constant with velocity in high-velocity O vi absorbers , suggesting that C iii resides in the same gas as the O vi . Collisional ionization equilibrium models with solar abundances can explain the O vi/C iii ratios for temperatures near 1.7 \times 10 ^ { 5 } K ; non-equilibrium models with the O vi “ frozen-in ” at lower temperatures are also possible . Photoionization models are not viable since they under-predict O vi by several orders of magnitude . The presence of associated C iii and H i strongly suggests the high-velocity O vi absorbers are not formed in the hotter plasma that gives rise to O vii and O viii X-ray absorption . We find that the shape of the O vi positive-velocity wing profiles is well reproduced by a radiatively cooling , vertical outflow moving with ballistic dynamics , with T _ { 0 } = 10 ^ { 6 } K , n _ { 0 } \approx 2 \times 10 ^ { -3 } cm ^ { -3 } , and v _ { 0 } \approx 250 km s ^ { -1 } . However , the outflow has to be patchy and out of equilibrium to explain the sky distribution and the simultaneous presence of O vi , C iii , and H i . We found that a spherical outflow can produce high-velocity O vi components ( as opposed to the wings ) , showing that the possible range of outflow model results is too broad to conclusively identify whether or not an outflow has left its signature in the data . An alternative model , supported by the similar multi-phase structure and similar O vi properties of highly ionized and 21 cm HVCs , is one where the highly ionized HVCs represent the low N ( H i ) tail of the HVC population , with the O vi formed at the interfaces around the embedded H i cores . Though we can not rule out the possibility that some high-velocity O vi absorbers exist in the Local Group or beyond , we favor a Galactic origin . This is based on the recent evidence that both H i HVCs and the million-degree gas detected in X-ray absorption are Galactic phenomena . Since the highly ionized HVCs appear to trace the interface between these two Galactic phases , it follows that highly ionized HVCs are Galactic themselves . However , the non-detection of high-velocity O vi in halo star spectra implies that any Galactic high-velocity O vi exists at z -distances beyond a few kpc .