In this study, we present results of a comprehensive computational and experimental study of CoFeVAl and CoFeV0.5Mn0.5Al Heusler alloys. It is shown that while CoFeVAl exhibits a fairly large degree of spin polarization, this material is not half-metallic due to the presence of the vanadium spin-down states at the Fermi level. However, replacing 50% of vanadium with manganese results in a nearly half-metallic transition, largely due to the shift of the Fermi level towards occupied states. Moreover, the half-metallicity of CoFeV0.5Mn0.5Al is rather robust in a wide range of considered mechanical strain and under experimentally observed B2-type atomic disorder, thus making this alloy potentially suitable for practical spintronic applications. Both considered alloys exhibit ferromagnetic alignment at larger lattice constants, aside from a relatively small magnetic moment of vanadium which is anti-aligned with the magnetic moments of Co, Fe and Mn. We have synthesized both CoFeVAl and CoFeV0.5Mn0.5Al alloys in cubic structure with some structural disorder using arc melting and annealing. The structural and magnetic properties of the synthesized CoFeV0.5Mn0.5Al alloy are in good agreement with the theoretical calculations but vary slightly from the parent compound.