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Density functional theory (DFT) calculations confirm that the structurallyordered Fe$_2$VAl Heusler alloy is nonmagnetic narrow-gap semiconductor. Thiscompound is apt to form various disordered modifications with highconcentration of antisite defects. We study the effect of structural disorderon the electronic structure, magnetic, and electronic transport properties ofthe full Heusler alloy Fe$_2$VAl and its off-stoichiometric equivalentFe$_2$VAl$_{1.35}$. Data analysis in relation to {\it ab initio} calculationsindicates an appearance of antisite disorder mainly due to Fe--V and Fe--Alstoichiometric variations. The data for weakly magnetic Fe$_2$VAl$_{1.35}$ arediscussed in respect to Ni$_2$VAl. Fe$_2$VAl$_{1.35}$ can be classified as anearly ferromagnetic metal with a pronounced spin glassy contribution, which,however, does not give a predominant effect on its thermoelectric properties.The figure of merit $ZT$ is at 300 K about 0.05 for the Fe sample and 0.02 forNi one, respectively. However, it is documented that the narrow $d$ bandresulting from Fe/V site exchange can be responsible for the unusualtemperature dependencies of the physical properties of the Fe2TiAl$_{1.35}$alloy, characteristic of strongly correlated electron systems. As an example,the magnetic susceptibility of Fe$_2$VAl$_{1.35}$ exhibits singularitycharacteristic of a Griffiths phase, appearing as an inhomogeneous electronicstate below $T_G\sim 200$ K. We also performed numerical analysis whichsupports the Griffiths phase scenario.

Off-stoichiometric effect on magnetic and electron transport properties of Fe$_2$VAl$_{1.35}$ in respect to Ni$_2$VAl; Comparative study