Beeswax oleogels (OGs), with a mechanical strength similar to pork backfat, were formulated with avocado (A), sunflower (S), and linseed (L) oils, applying a central composite design plus star point, and were evaluated as oral delivery vehicles of curcuminoids (OGACur, OGSCur, OGLCur). The incorporation of curcumin into the OG matrix significantly delayed both the formation of peroxides and conjugated trienes (K₂₆₈ values), and the degradation rate of curcumin decreased with the increase of the oil polyunsaturated fatty acids (PUFA) content. The oil structuring did not affect the bioaccessibility of curcuminoids (>55% in all the OGs, regardless of the oil type), but it did reduce the release of fatty acids (~10%) during in vitro gastrointestinal digestion. The intestinal absorption, evaluated in Caco-2 cell monolayers, was higher for the micelle-solubilized curcumin from the digested OG than from unstructured oils, and it showed high anti-inflammatory potential by inhibiting the tumor necrosis factor-α (TNF-α) production compared to the positive control, both before and after the stimulation of ThP-1 cells with LPS. Regardless of the oil type, these beeswax-based OGs with gel-like behavior designed as fat replacers may be promising vehicles for the oral delivery of curcuminoids.