The magnetization, crystal structure, and thermal expansion of a nearly stoichiometric Sr_1.04(3)Er_2.09(6)O_4.00(1) single crystal have been studied by PPMS measurements and in-house and high-resolution synchrotron X-ray powder diffraction. No evidence was detected for any structural phase transitions even up to 500 K. The average thermal expansions of lattice constants and unit-cell volume are consistent with the first-order Grüneisen approximations taking into account only the phonon contributions for an insulator, displaying an anisotropic character along the crystallographic a, b, and c axes. Our magnetization measurements indicate that obvious magnetic frustration appears below ∼15 K, and antiferromagnetic correlations may persist up to 300 K.