Magnetodielectric (MD) properties of as-prepared (AP) and air-annealed Bi1-xCaxFe1-yTiyO3-δ nanoparticle ceramics made by spark plasma sintering process are investigated as a function of temperature. Aliovalent Ca2+ substitution at Bi3+ site creates oxygen vacancies (VO) in the lattice disrupting the intrinsic spin cycloid of BiFeO3, which are suppressed when the charge compensating Ti4+ is co-substituted. In addition, cation substitution reduces the grain size and increases surface oxygen vacancies. These lattice and surface VO defects play a significant role in enhancing the magnetic properties. Zero-field-cooled magnetization curves of all AP samples show a sharp Verwey-like transition at 120 K, which weakens on air-annealing. A coexistence of positive and negative MD [MD = ΔÉ(H)É(H=0); ΔÉ(H)=É(H)-É(H=0)] response is observed, with the former dominating at 300 K and the latter at 10 K. As-prepared 5 at.% (10 at.%) Ca and Ca-Ti substituted BiFeO3 ceramics exhibit a maximum MD response of-10% (+3%) at 10 K (300 K). Negative MD response diminishes for air-annealed Bi1-xCaxFe1-yTiyO3-δ ceramics due to the reduction in VO concentration. Samples exhibiting dominant positive MD response show a similar trend for MD vs H and M2 vs H plots. This agreement between M2 and ΔÉ(H) demonstrates a strong inherent MD coupling. On the contrary, negative MD does not follow this trend yet shows a linear relationship of MD vs M2, suggesting a strong coupling between the magnetic and dielectric properties. Temperature-dependent MD studies carried out at 5 T show a gradual change from negative to positive values. Negative MD at low temperatures could be activated by the spin-lattice coupling, which dominates even at high frequency (1 MHz) under the applied field. Other contributions, including Verwey-like transition, magnetoresistance, and Maxwell-Wagner effects, do not influence the observed MD response. A prominent role of oxygen vacancies in altering the MD behavior of BiFeO3 is discussed in detail. © 2021 American Physical Society.