The static characteristics of 850 nm-range vertical-cavity surface-emitting lasers (VCSEL) based on strained InGaAs/AlGaAs quantum wells were studied in the wide range of oxide current aperture sizes and the origins of their anomalous behavior at large gain-to-cavity detuning was analyzed. The higher-order modes localized at the periphery of the oxide current aperture can appear in the studied VCSELs due to the lateral carrier spreading in the quantum wells and the specific profile of the oxide aperture (leading to the formation of a two-stage effective waveguide). Inhomogeneous carrier injection over the current aperture area in wide-aperture lasers leads anomalous start of lasing via high-order transverse modes, and the subsequent transition to the classical lasing via low-order modes with an increase in the current is due to a change of the gain-to-cavity detuning with an increase in the internal laser temperature. Anomalous lasing via higher-order modes in the case of narrow-aperture VCSELs becomes possible due to the increase in diffraction losses at the edge of the oxide current aperture for the fundamental mode, while the subsequent switching to the two-mode lasing is due to not only a decrease in the gain-to-cavity detuning, but also the thermal lens effect.