Would it be a good idea to multilevel them?
What changes are there when compared to normal levels?

As someone else said in another post they seem to just be roughly 3x harder then normal. The main bonus is the superpower they give you but the AP/day seems to work out to be roughly the same so they aren't any better then a normal level besides the special power.

I'd save my multilevels only for Trisk, USA and Europe

May I hi-jack this topic to ask how to unlock the final hardened level? I'm at Asia: Population Density at the moment and before the update I had activated enough skip levels that all but the final level were unlocked. After the update I could access all but the final hardened level. Today I unlocked the final level with another SL (from daily reward) but the final hardened level is still unlocked and the game prevents me from spending another SL for the hardened level.

TLDR: All but the final hardened level got unlocked automatically although for half of the hardened levels I haven't even finished their normal version. The final hardened level won't unlock by unlocking the final normal level.

You have to unlock one more...

Well, as I said, there is no more to unlock. Does that mean, you can only unlock the final hardened level by completing the final normal level?

No, you have to unlock it like any other level. Use a Skip Level and it will be available.

I suspect the hard level only unlock once you beat the normal level. Since you already unlocked the normal levels except for the last one, their hard level unlocked with the update to prevent you from having to beat all those levels again.

Since you didnt have the last level unlocked when you updated, the hard level didnt autounlock so you will have to beat the normal level to unlock it.

So why is it a bad idea to multilevel them?

It's not. The normal goal of using multilevels is to get the most extra AP per unit time you can, which means multileveling the levels that will take you the longest. Hardened Triskelion and Hardened Europe Huge are the best bang for your buck for multileveling currently.