Nope. You can equip items from expansions you do not own.
As for aquiring the expansions themselves, even if you'er startign fresh with low level characters, I highly recommend DoN for the guild hall and guild lobby, the bandolier, and the potion belt, and depths of darkhollow for the shrouds and monster missions.
Omens of War, however, does not feature anything you need to worry about until level 45 or later.