In this work we combine spectroscopic information from the SkyMapper survey for Extremely Metal-Poor stars stars and astrometry from Gaia DR2 to investigate the kinematics of a sample of 475 stars with a metallicity range of -6.5<=[Fe/H]<=-2.05 dex. Exploiting the action map, we identify 16 and 40 stars dynamically consistent with the Gaia Sausage and Gaia Sequoia accretion events, respectively. The most metal-poor of these candidates have metallicities of [Fe/H]=-3.31 and [Fe/H]=-3.74 , respectively, helping to define the low-metallicity tail of the progenitors involved in the accretion events. We also find, consistent with other studies, that 21% of the sample have orbits that remain confined to within 3kpc of the Galactic plane, i.e., |Zmax|<=3 kpc. Of particular interest is a sub-sample (11% of the total) of low |Zmax| stars with low eccentricities and prograde motions. The lowest metallicity of these stars has [Fe/H] = -4.30 and the sub-sample is best interpreted as the very low-metallicity tail of the metal-weak thick disk population. The low |Zmax|, low eccentricity stars with retrograde orbits are likely accreted, while the low |Zmax|, high eccentricity pro- and retrograde stars are plausibly associated with the Gaia Sausage system. We find that a small fraction of our sample (4% of the total) is likely escaping from the Galaxy, and postulate that these stars have gained energy from gravitational interactions that occur when infalling dwarf galaxies are tidally disrupted.