Oh gosh, there's a lot going on there. Maybe started with a stony semi matt white glaze over all and then from the 3rd photo that views the vase from the top angle, it looks like they partially dipped in other glaze/glazes cuz of the lines. The pink looks like it possibly comes from chrome ox so maybe a wash was applied? The tan might be rutile breaking in the blue glaze or maybe a wash applied as well. Looks like a warmer stoneware clay than white, and if it was made by a studio potter rather than manufactured, I'd guess fired cone 10 in a gas kiln but pretty oxidized.
Sorry I couldn't be more help. Looks like you'll have a challenging project on your hands. Best of luck!