The interface and transport properties of Fe/V/MgO/Fe and Fe/V/Fe/MgO/Fe magnetic tunneling junctions are investigated by using density-functional theory and nonequilibrium Green's-function methods. Bader analysis reveals that the Fe layer at the interface with MgO loses a small amount of charge with respect to its bulk value, in contrast to a previous study [W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J. M. MacLaren Phys, Rev. B 63, 054416 (2001)]. At the same time at the Fe/V interface a magnetic moment is induced on the V layer by proximity. Importantly, the direction of the magnetization of the first V monolayer immediately close to the MgO barrier oscillates with the total V-layer thickness and the relative stability of a particular magnetic configuration weakens as such a thickness is increased. These two aspects pose a challenge to the Fe/V/MgO/Fe device signal stability. A more intriguing situation is found for Fe/V/Fe/MgO/Fe junctions. Their transport properties depend sensitively on the thickness of the Fe layer intercalated between V and the MgO barrier. This is the result of resonances through quantum-well states of ${\ensuremath{\Delta}}_{1}$ symmetry localized in the intercalated Fe layer. In particular, for some geometries we find a massive magnetoresistance obtained by simply switching the direction of the magnetization of the Fe interlayer, while keeping the direction of the electrodes fixed. This effect may be employed in the design of new spin valves with extremely high spin polarization but still relatively large current densities.