In marine seismic exploration, seismic signals comprise primaries that undergo first-order scattering, as well as multiples resulting from multi-order scattering events. Surface-related multiples involve multi-order scattering at the free surface interface between seawater and air and exhibit a smaller reflection angle and broader illumination compared to primaries. Internal multiples, originating from multi-order scattering among stratified layers, provide additional illumination compensation beneath the reflecting interface. However, in conventional primary migration, different-order wavefields may result in crosstalk artifacts. To address this issue, we developed a least-squares migration (LSM) method based on the multi-order wavefield global normalization condition. This methodology investigates the illumination effects and crosstalk artifacts associated with different-order surface-related and internal multiples, and then modifies the global normalization condition by incorporating an illumination compensation perspective. Virtual sources, represented by surface-related multiples and internal multiples, are integrated into the source compensation term, ultimately yielding a multi-order wavefield normalization condition. This normalization condition is subsequently combined with least-squares full-wavefield migration (LSFWM). Numerical experiments demonstrate that the normalization condition of multi-order wavefields can resolve the problem of weak deep imaging energy and promote the suppression of multiple crosstalk artifacts in the least-squares algorithm.