We study structural properties of WLg,theta q,p, which are Wiener-Lebesgue spaces with respect to a slowly varying metric g and with parameters p, q is an element of (0,infinity], theta is an element of R. For p is an element of (0, 1], we deduce Schatten-p properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable WLg,theta q,p-boundedness conditions. Especially, we perform such investigations for the Weyl-Hormander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.