FUSE spectra of 100 extragalactic objects are analyzed to obtain measures of O VI absorption along paths through the Milky Way thick disk/halo. Strong O VI absorption over the approximate velocity range from -100 to 100 km/s reveals a widespread but highly irregular distribution of thick disk O VI, implying the existence of substantial amounts of hot gas with T ~ 3x10^5 K in the Milky Way halo. Large irregularities in the distribution of the absorbing gas are found to be similar over angular scales extending from less than one to 180 degrees, indicating a considerable amount of small and large scale structure in the gas. The overall distribution of Galactic O VI is not well described by a symmetrical plane-parallel layer of patchy O VI absorption. The simplest departure from such a model that provides a reasonable fit to the observations is a plane-parallel patchy absorbing layer with a scale height of 2.3 kpc, and a 0.25 dex excess of O VI in the northern Galactic polar region. The O VI absorption has a Doppler parameter b = 30 to 99 km/s, with an average value of 60 km/s . Thermal broadening alone cannot explain the large observed profile widths. The average O VI absorption velocities toward high latitude objects range from -46 to 82 km/s, with a sample average of 0 km/s and a standard deviation of 21 km/s. O VI associated with the thick disk moves both toward and away from the plane with roughly equal frequency. A combination of models involving the radiative cooling of hot fountain gas, the cooling of supernova bubbles in the halo, and the turbulent mixing of warm and hot halo gases is required to explain the presence of O VI and other highly ionized atoms found in the halo. (abbreviated)
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