You cannot drag-and-drop items in The Elder Scrolls IV: Oblivion on Xbox 360. The console UI uses a cursorless, list-based menu system. Here's the efficient workflow:
PC has drag-and-drop, mouse wheel scrolling, quick keys (1-8), and UI mods (DarNified UI, BTUI). If you have a laptop/Steam Deck, the PC version is vastly superior for inventory management.