Battle difficulty is a fairly easy empirical test. Find an isolated unit somewhere. Make sure it's of a type that your faction can field. Teleport the AI faction's unit (Captain Somebody-or-other, by definition, so for most AI factions this should be easy) to a convenient location, and if you don't have a counterpart unit, spawn one with create_unit. Fight. If the AI crushes you, you're on H or VH battle difficulty. If you care which of the two it is, I'd suggest doing this a few times, keeping track of the loss ratio statistics, and then calibrating by doing the same in fresh test campaigns where you've set the battle difficulty to H and VH respectively.

In practice, you can also just play the campaign for a while. If you're used to M battle difficulty and the campaign is on H or VH, you'll eventually notice a trend that your troops aren't performing as well as they should.

For campaign difficulty, naval battles are probably the best test. I believe auto-resolve is set by campaign difficulty, not battle difficulty. If you see pirate fleets giving quinquiremes a tough fight, you're probably on VH. Pirates have easy names, so teleport as many as you like to set up your test battles. I've never played RTR (barely have time for EB sometimes...), so if there are no pirates I guess you're stuck with whatever AI navies exist for your test opponents. You could try land battle auto-resolves too, but that could be inconclusive - I've seen ridiculous outcomes even when I know the campaign is M. Again, calibrating to equivalent test cases done in other campaigns of known difficulty would be prudent.