Structurally ordered piezoelectric Ca3TaGa3Si2O14 (CTGS) single crystals are studied. The elastic and piezoelectric constants are determined in the temperature range from 20 degrees C to 900 degrees C by two independent approaches: resonant and pulse-echo acoustic methods. Further, the temperature dependent acoustic losses are examined. These investigations reveal two loss peaks with maxima near 68 degrees C and 416 degrees C at 4.5 MHz that are attributed to anelastic point defect relaxations. Further, the transport of oxygen is investigated using the isotope O-1(8) as a tracer at temperatures from 1000 degrees C to 1200 degrees C. It is shown that the oxygen self-diffusion coefficients are at least three orders of magnitude lower than those of langasite, which is one reason for relatively low losses in CTGS at temperatures on the order of 1000 degrees C. Finally, the long-term stability of fundamental materials properties including electrical conductivity and resonance frequency is examined at 1000 degrees C. After one year of thermal treatment, the resonance frequency of resonators made from crystals of different sources is found to decrease only between 0.1% and 0.4%.