We report the temperature-dependent optical conductivity and angle-resolved photoemission spectroscopy (ARPES) studies of the multiband iron-based superconductor Sr0.67Na0.33Fe2As2. Measurements were made in the high-temperature tetragonal paramagnetic phase, below the structural and magnetic transitions at TN≃125 K in the orthorhombic spin-density-wave (SDW)-like phase and Tr≃42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDW order exist, and below the superconducting transition at Tc≃10 K. The free-carrier component in the optical conductivity is described by two Drude contributions: one strong and broad and the other weak and narrow. The broad Drude component decreases dramatically below TN and Tr, with much of its strength being transferred to a bound excitation in the midinfrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone folding below Tr. Below Tc the dramatic decrease in the low-frequency optical conductivity signals the formation of a superconducting energy gap. ARPES reveals holelike bands at the center of the Brillouin zone (BZ), with both electron- and holelike bands at the corners. Below TN, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; however, below Tr the electronlike bands shift and split, giving rise to a low-energy excitation in the optical conductivity at ≃20 meV. The C2 and C4 magnetic states, with resulting spin-density-wave and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets but appears to have relatively little impact on the superconductivity in this material.