Hydrothermal and exergy characteristics are numerically studied for the laminar flow in compact double-pipe heat exchangers (DPHXs) equipped with tube-side helical insert and annulus-side helical strip. Helical screw-type tape inserts are placed in the tube-side of the heat exchanger, along with four different configurations of helical strip in the annulus-side. Heat transfer enhancement is observed for all studied configurations of DPHX compared to the plain DPHX. The helical inserts and strips increase the effective surface area, and also create secondary flows and higher mixing in tube- and annulus-side. Considering the overall heat transfer coefficient of the DPHXs as the comparison criterion, the optimum configuration is selected. A comprehensive parametric analysis is conducted on the optimum configuration to study the effect of relevant operating and geometrical parameters. Increasing the number of helical periods and helical fins in the tube- and annulus-side leads to enhanced overall heat transfer coefficient of DPHXs. The effect of using alumina–water nanofluid flowing in the tube-side is investigated for the optimum configuration. The rate of overall heat transfer enhancement is found to be higher in configurations with more intense mixing, due to more uniform nanoparticle distribution. Exergy analysis is performed to obtain the exergy efficiency of the DPHXs with different configurations. The effect of different operating and geometrical parameters on the exergy efficiency is investigated for the optimum configuration.