Computation-Enabled Object Storage (COS) systems, such as MinIO and Ceph, have recently emerged as promising storage solutions for post hoc, SQL-based analysis on large-scale datasets in High-Performance Computing (HPC) environments. By supporting object-granular layouts, COS facilitates column-oriented access and supports in-storage execution of data reduction operators, such as filters, close to where the data resides. Despite growing interest and adoption, existing COS systems exhibit several fundamental limitations that hinder their effectiveness. First, they impose rigid constraints on output data formats, limiting flexibility and interoperability. Second, they support offloading for only a narrow set of operators and expressions, restricting their applicability to more complex analytical tasks. Third--and perhaps most critically--they fail to incorporate design strategies that enable compute offloading optimized for the characteristics of deep storage hierarchies. To address these challenges, this paper proposes OASIS, a novel COS system that features: (i) flexible and interoperable output delivery through diverse formats, including columnar layouts such as Arrow; (ii) broad support for complex operators (e.g., aggregate, sort) and array-aware expressions, including element-wise predicates over array structures; and (iii) dynamic selection of optimal execution paths across internal storage layers, guided by operator characteristics and data movement costs. We implemented a prototype of OASIS and integrated it into the Spark analytics framework. Through extensive evaluation using real-world scientific queries from HPC workflows, OASIS achieves up to a 32.7% performance improvement over Spark configured with existing COS-based storage systems.