High quality Fe/γ-Fe2O3 core/shell, core/void/shell, and hollow nanoparticles with two different sizes of 8 and 12 nm were synthesized, and the effect of morphology, surface and finite-size effects on their magnetic properties including the exchange bias (EB) effect were systematically investigated. We find a general trend for both systems that as the morphology changes from core/shell to core/void/shell, the magnetization of the system decays and inter-particle interactions become weaker, while the effective anisotropy and the EB effect increase. The changes are more drastic when the nanoparticles become completely hollow. Noticeably, the morphological change from core/shell to hollow increases the mean blocking temperature for the 12 nm particles but decreases for the 8 nm particles. The low-temperature magnetic behavior of the 12 nm particles changes from a collective super-spin-glass system mediated by dipolar interactions for the core/shell nanoparticles to a frustrated cluster glass-like state for the shell nanograins in the hollow morphology. On the other hand for the 8 nm nanoparticles core/shell and hollow particles the magnetic behavior is more similar, and a conventional spin glass-like transition is obtained at low temperatures. In the case of the hollow nanoparticles, the coupling between the inner and outer spin layers in the shell gives rise to an enhanced EB effect, which increases with increasing shell thickness. This indicates that the morphology of the shell plays a crucial role in this kind of exchange-biased systems.