The magnetic field distribution of the vortex lattice of optimally doped La_1.84Sr_0.16CuO₄ thin films of various thicknesses, grown on different substrates, was investigated. The influence of film thickness and biaxial strain on the magnetic penetration depth and the superconducting number density were studied using muon spin rotation and compared to single-crystal results. We found an effective superconducting layer thickness smaller than the total film thickness, implying that the interfaces of the films are not or less superconducting than the bulk of the film. The superfluid density diminished in thinner films whereas compressive strain enhanced it. This shows that the number density of superconducting carriers is strongly affected by the boundary conditions as well as by the strain. Furthermore, in fully relaxed optimally doped La_1.84Sr_0.16CuO₄ films grown on SrTiO₃, we found a low-temperature magnetic state which sets in at T_c. It is reasoned that defects at the surface slow down high-frequency magnetic fluctuations such that a "quasistatic" magnetic ground state results, which coexists with the diminished surface superconductivity. These results indicate that the properties of the surface of optimally doped La_1.84Sr_0.16CuO₄ superconductors differ substantially from the bulk.