When you play Oblivion, the "final showdown" between Martin and Dagon occurs in 3E433 (or 3E434 depending on how slowly you progress the Main Quest). The calendar in the game continues as 3E433/4, rather than switching to 4E1 straight away. I assume that recognition of a new era might require some official pronouncement, and the absence of an Emperor could delay that. So when would people generally start using the new Era's dates?

When Ocato declared it did. Probably not long after.