In high entropy alloys (HEAs), the addition of large-size atoms results in lattice distortion and further leads to solid solution strengthening or precipitation strengthening. However, the relationship between atomic radius, solid solution strengthening and precipitation strengthening has not been discerned yet. In this work, CoCrFeNiX_0.4 (X = Al, Nb, Ta, with an equi-atomic radius) HEAs were prepared by powder plasma arc additive manufacturing (PPA-AM) and evaluated for their mechanical properties. Compression and nano-indentation hardness tests showed that the HEA with Ta showed the best properties. The influence of atomic radius and solid solubility on solid solution strengthening was investigated and the main strengthening mechanism that determines the mechanical properties of the developed HEAs was analyzed. The results showed that (i) the CoCrFeNiAl_0.4 alloy did not show any solid solution strengthening effect and that a clear relation between solid solution strengthening and atomic size was not observed; (ii) in both CoCrFeNiTa_0.4 and CoCrFeNiNb_0.4 HEAs, precipitation strengthening and grain boundary strengthening effects are observed, wherein the difference in mechanical properties between both the alloys can be mainly attributed to the formation of fine eutectic structure in CoCrFeNiTa_0.4; and (iii) from the microstructural analyses, it was identified that, in the CoCrFeNiTa_0.4 HEA, the location containing a fine eutectic structure is accompanied by the formation of low-angle grain boundaries (LAGBs), which is also the region where deformed grains gather, giving rise to improved mechanical strengthening.