Refractory metals and their alloys are promising, as they possess high-temperature strength and melting points at elevated temperatures. But the fundamental limitation associated with these metals is high-temperature oxidation. The literature mentions that the Ti, Zr, and Hf dissolve oxygen atoms up to 33 at.%, 29 at.%, and 20 at.% respectively, in the octahedral interstitial site of the HCP metal system. This has led to investigations on understanding the behavior of oxygen in an octahedral interstitial site just after penetrating in refractory metals and alloys. In the present work, the first principle DFT calculations were done to report the oxygen interstitial formation energy (OIFE) of 9 refractory metals, such as Ti, Zr, Hf, V, Nb, Ta, Mo, W, and Re, and 25 equiatomic BCC binary alloy systems, such as V-Ti, Nb-Ti, Ta-Ti, Mo-Ti, W-Ti, Nb-Zr, Ta-Zr, Mo-Zr, Nb-Hf, Ta-Hf, Mo-Hf, W-Hf, Nb-V, Ta-V, Mo-V, W-V, Mo-Nb, W-Nb, Re-Nb, Nb-Ta, Mo-Ta, W-Ta, W-Mo, Re-Mo, and W-Re. The OIFE for an alloy system was reported for 7 different octahedral sites, such as 0-6, 1-5, 2-4, 3-3, 4-2, 5-1, and 6-0, based on the number of atoms of A-type and B-type around oxygen interstitial as an octahedral nearest neighbor(octa-NN). The variation in OIFE with change in the atoms of A-type and B-type at the third nearest neighbors (3NN) was also checked for 0-6 and 6-0 sites, and it was observed that the contribution of atoms at 3NN was minimal. The OIFE decreases with an increase in the number of atoms of B-type around the oxygen interstitial as octa-NN, following the trend of composition averaged OIFE calculated from OIFE of individual elements. In most of the cases, the OIFE of 0-6 site was minimum when the O interstitial was surrounded by all the atoms of B-type, which have low OIE in their pure bulk form, and the OIE of 6-0 site was maximum when the O interstitial was surrounded by all the atoms of A-type, which have relatively higher OIE in their pure bulk form when compared to atoms of B-type. It is not the composition averaged OIFE that determines the stability of oxygen interstitial in alloys, but it is the presence of low OIFE elements as clusters around octahedral neighbor locally that determines it. It is because, the contributions to OIFE comes from octa-NN and the contributions from 3NN is relatively minimal. The presence of low OIFE element around oxygen interstitial at octa-NN and slightly in 3NN would make the oxygen behave as if it were in the bulk of low OIFE element, making the system prone to oxidation.