Is it possible to see which Oblivion mods a save relies on?

Yes! Wrye Bash has a savefile browser tab that will show you a save's "master list", which is the list of mod files (and their order) that the save file depends on for all its object IDs.

Oblivion mod manager http://www.tesnexus.com/downloads/file.php?id=2097

This is a utility for managing plugins, and also for packing them for distribution. It can be used either as an enhanced version of the oblivion launcher's data files selector, or as a more advanced mod manager when mods are specially packed into omod files.

Also included are several utilities, such as a BSA unpacker, save file manager for syncing your active plugin list to a save game, conflict detector, archiveinvalidation.txt generator and more.