Although the Hubble constant $H_0$ and spatial curvature $Omega_{K}$ have been measured with very high precision, they still suffer from some tensions. In this paper, we propose an improved method to combine the observations of ultra-compact structure in radio quasars and strong gravitational lensing with quasars acting as background sources to determine $H_0$ and $Omega_{K}$ simultaneously. By applying the distance sum rule to the time-delay measurements of 7 strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers, we obtain stringent constraints on the Hubble constant ($H_0=78.3pm2.9 mathrm{~km~s^{-1}~Mpc^{-1}}$) and the cosmic curvature ($Omega_K=0.49pm0.24$). On the one hand, in the framework of a flat universe, the measured Hubble constant ($H_0=73.6^{+1.8}_{-1.6} mathrm{~km~s^{-1}~Mpc^{-1}}$) is strongly consistent with that derived from the local distance ladder, with a precision of 2%. On the other hand, if we use the local $H_0$ measurement as a prior, our results are marginally compatible with zero spatial curvature ($Omega_K=0.23^{+0.15}_{-0.17}$) and there is no significant deviation from a flat universe. Finally, we also evaluate whether strongly lensed quasars would produce robust constraints on $H_0$ and $Omega_{K}$ in the non-flat and flat $Lambda$CDM model if the compact radio structure measurements are available from VLBI observations.
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