Structural and magnetic studies on SrLa(Fe0.25Mn0.25)Co0.5O4 (FMC1) and SrLaFe0.5(Mn0.25Co0.25)O4 (FMC2) reveal unusually large exchange bias behavior in these atomically disordered quasi-two-dimensional layered perovskites. Powder x-ray as well as neutron diffraction confirm tetragonal crystal structure with I4/mmm space group for both the compounds. Magnetization measurements on FMC1 as well as FMC2 reveal short-range antiferromagnetic ordering around room temperature and frozen magnetic clusters at lower temperatures (T<23K for FMC1 and T<43K for FMC2). The random occupancy of mixed-valent magnetic ions (Fe3+/Fe4+, Mn3+/Mn4+, Co2+/Co3+) at the perovskite octahedral sites give rise to locally varying competing antiferromagnetic and ferromagnetic exchange interactions, resulting in low temperature frozen spin states. Giant exchange bias values of ∼6 and ∼9.5 kOe were observed for FMC1 and FMC2, respectively, at 2 K under an applied field of 50 kOe. In comparison, the Co-rich FMC1 exhibits higher magnetization and coercivity, whereas Fe-rich FMC2 possesses a higher exchange bias effect. Our experimental results reveal compositional tuning induced exotic magnetic behavior in quasi-two-dimensional layered oxides. © 2020 American Physical Society.