Odžić was born in 1968 in Novi Sad, SAP Vojvodina, SR Serbia, SFR Yugoslavia.
[1] He is employed at JVP Vode Vojvodine as an independent professional associate for safety, occupational health and fire protection.
Odžić started his political career as a member of the centre-left League of Social Democrats of Vojvodina (LSV).
[2][3] Beginning in 2021, Odžić and the Vojvodina Front have campaigned on introducing "Vojvodinian" as a nationality for the 2022 census.
However, their campaign went unsuccessful, considering that "Vojvodinian" retained its status as a regional identity, and not a national one.