We report on spin-polarized density-functional theory study of adsorption of dihalogen molecules X2 (X = F, Cl, Br and I) on the Fe/W(110) substrate, i.e., X2/Fe/W(110) systems. We considered different molecular orientations and adsorption sites of the halogens and obtained their corresponding ground-state structures. We obtained initial molecular orientation (IMO) and initial adsorption site (IAS), i.e., IMO-IAS combinations that give the minimum energy configurations for each of the X2/Fe/W(110) systems. Our results shows that all the molecules studied in this work are chemisorbed on the Fe surface. Also, the halogen atoms may be adsorbed dissociatively on the hollow sites in such a way that an X2 separates into two X atoms with each of the atoms located at two nearby hollow sites. Similarly, we found IMO-IAS combinations which resulted in a non-dissociative adsorption. In the latter, the pre-relaxed IMO-IAS is maintained even after the structural relaxation. The most stable configuration for the X2 dihalogen molecule in this case is either the top or bridge site while the halogen is in perpendicular orientation to the Fe surface. We conclude therefore that, the final relaxed configurations of the X2 halogen depends on the IMO through which is deposited on the Fe/W(110) substrate. The trend in the adsorption energy EA for the most stable configurations for the dissociative adsorption is EA (F) > EA (Cl) > EA (Br) > EA (I). The trend of EA for non-dissociative adsorption is similar to that of dissociative adsorption, however, the latter is the more energetically favorable. Electronic structure calculations show hybridization between the p and d orbitals of X and Fe atoms respectively. Furthermore, we have found antiferromagnetic coupling between the interfacial W atoms and the Fe overlayer atoms while ferromagnetic coupling is found between the halogens and the Fe atoms. Our work represents a detailed study of adsorption properties of highly reactive halogens in contact with the Fe/W(100) surface.