We present a detailed study of structural, magnetic and thermodynamic properties of a series of Heusler alloys Fe2-xMnxCrAl (x = 0, 0.25, 0.5, 0.75 and 1). Structural investigation of this series is carried out using high resolution synchrotron X-ray diffraction. Results suggest that with increasing Mn concentration, the L21 structure of Fe2CrAl is destabilized. The DC magnetization results show a decrement in paramagnetic (PM) to ferromagnetic (FM) phase transition temperature (TC) with increasing Mn concentration. From the systematic analysis of magnetic memory effect, heat capacity, time dependent magnetization, and DC field dependent AC susceptibility studies it is observed that, Fe2CrAl exhibits cluster glass(CG)-like transition approximately at 3.9 K (Tf2). The alloys, Fe1.75Mn0.25CrAl and Fe1.5Mn0.5CrAl exhibit double CG-like transitions near Tf1 ~ 22 K, Tf2 ~ 4.2 K and Tf1 ~ 30.4 K, Tf2 ~ 9.5 K respectively, however, in Fe1.25Mn0.75CrAl, a single CG-like transition is noted at Tf2 ~ 11.5 K below TC. Interestingly, FeMnCrAl shows the absence of long ranged magnetic ordering and this alloy undergoes three CG-like transitions at ~22 K (Tf*), 16.6 K (Tf1) and 11 K (Tf2). At high temperatures, a detailed analysis of temperature response of inverse DC susceptibility clearly reveals the observation of Griffiths phase (GP) above 300 K (T*) in Fe2CrAl and this phase persists with Mn concentration with a decrement in T*.