Recently, various types of porous surfaces have been demonstrated for lubricant (e.g., oil) impregnated omniphobic surfaces. However, the retention of the lubricating liquid within the porous layer and the omniphobic durability still remain challenges. Here, the omniphobic durability of the oil-impregnated surfaces of various types of anodic aluminum oxide (AAO) nanostructures is investigated. The oil impregnation into nanoporous AAO with high porosity enhances droplet mobility by eliminating the pinning site of a contact line on the solid surface, whereas that with low porosity allows the pinning site to result in less mobility. In the cases of nanopillared AAO layers, although the oil-impregnation enhances the repellency to liquids, oil is prone to be depleted by external force such as fluid flow due to the nature of the interconnected oil through the passages between pillars, which limits the omniphobic durability. Among the various types of nanostructured AAO surfaces, the AAO with isolated pore geometry with high porosity exhibits the most durable omniphobicity for a wide range of liquids including organic liquids with low surface tensions. Moreover, the nanoporous AAO surface shows great anti-bacterial adhesion property, reducing the adhesion of bacteria (Escherichia coli K-12) up to 99.2% compared to a bare aluminum surface.