In the mixed crystal K1-xLixTaO3 the off-center Li+ ions carry an electric dipolar moment, coupled to electric fields, and an elastic quadrupolar moment, coupled to elastic strains. We have performed acoustic and dielectric measurements, in crystals with x = 1.7% (T-c = 35 K) and x = 5% (T-c = 75 K). In particular, we have studied the relaxation of the Li+ ions, which manifests itself on both the dielectric constant and the elastic constant by a peak in the imaginary part and a step in the real part. In the less concentrated crystal, the dielectric results are analyzed in the form of Argand (Cole-Cole) diagrams exhibiting a very particular (strophoidal) shape, from which an unusual and temperaturedependent distribution of the relaxation times is deduced. In the second crystal we have studied the time-dependent effects, the effect of the cooling-rate and the thermal hysteresis under T-c. All features indicate a first-order-like transition, which is clearly observed by both techniques.