Which province did good during the oblivion crisis, and which one didn't? I know Black Marsh and Summerset Isle did pretty good, Morrowind not so much. Are there any books or npc that says how well did the other provinces did during the crisis?

This is my prediction on how well each province did

Black Marsh - Did really good since they swarmed the daedras and forced them to shut down their own gates.
Morrowind - Did alright, had one major redoran city destroyed but they put up a good fight and the Telvanni were closing gates.
Cryodill - Did ok, had a city destroyed but they had the aid of the CoC.
Hammerfell - I think they did good since they were able to fight the Thalmors to a standstill. The daedra invaders probably got lost in the dessert while being swarmed by dessert warriors/aiki or swallowed by quicksand.
Valenwood - Think they did good since they got the forest field advantage plus mass amount of wood elf archers should be able to gun down many many daedras.
Summerset Isle - Did alright at the beginning but after the Thalmors took over, they started to kick ass.
Skyrim - Think they did alright, The jarls forces and clans probably gave them a good beatdown.
Elsweyr - They probably did ok, their sneaky tactics should surprised the daedras, and they got the fury of the sands on their side.
High Rock - Should had done pretty well since they got a pretty decent strong military there.

Er, Crystal-Like-Law was collapsed by the daedra. If that's doing "alright" then I don't want to know what doing badly would look like.

It'd look like lots of lava, and a marginal increase in the number of dead babies.

It's really hard to say. We know both Cyrodiil and Morrowind lost a city. We know that the Telvanni in Morrowind closed gates, and we know that the CoC helped the armies in Cyrodiil close gates. Black Marsh appearantly did great. Summerset didn't do so well, losing Crystal-like-law... So I'd say they suffered terrible.

I don't think we have any word on other towns and provinces... We do know Skyrim didn't exactly lose mayor cities so that must mean they did okay. I don't think we can really speculate on other provinces.

You'd think that High Rock would do okay because of the relatively large group of mages and quality of armies, but you'd think the same about Summerset and they obviously didn't do okay.

I would imagine that being in a forest would actually be bad for the Bosmer; the Daedra in Oblivion certainly seemed to have a knack for burning things...

I'm not so sure that the whole "Agonians Swarming the Deadlands" thing is anything but exageration and propoganda by the An-Xileel.
Firstly, the only evidence we has of this actually happening (that I can recall) is a single, half drunken conversation between a rather young Argonian (not old enough to have lived during the Crisis) and a rather young Breton (again, not old enough to have lived during the Crisis).
Secondly, Daedra are immortal, they'd come back eventually.
Thirdly. It seems they weren't good enough to close the gates themselves, it is said that Dagon's lieutenants closed the gates, which means the Argonians didn't advance far enough into the gate to reach the sigil stone or even the tower.
Lastly, even if they somehow hadn't figured out to pick up the noisy stone, what could they do? Can Argonains swim through lava now?

So I think that very few, if any, of the Gates were closed by Dagon's lieutenants due to the Argonian's "ferocity" and that the gates being closed coincided with Martin's shattering of the Amulet of Kings. So the An-Xileel just used the closing of the gates as a political tool to unite the Argonians and force the Empire out of their swamps.

In Oblivion one of the rumours you could hear was that many Argonians had received 'the Calling' and had returned to Black Marsh.

Dont underestimate the Hist.
I think that of all the provinces Black Marsh probably faired the best.
We know that Argonian physiology is in large part determined by the Hist.
It is not unlikely that the Hist indeed transformed (some) Argonians into fierce warrior-lizards. I imagine them to have ended up looking like something out of jurassic park, though maybe with more spikes, as, you know, spikes are cool

What is said about the war as I recall (no idea of what source I got it from) is that the Argonians launched an attack so fierce that the gates were closed by the daedra in order to keep them out.
It must have been like expecting to unleash hell and terror only to find youd opened a gate to an even worse hell dimension.

The daedra are immortal, but returning to a corporeal status is lengthy and painful. This is why they ally themselves to a Daedra lord as they have the ability to make it less so, but it is still not instant.

Black Marsh was capable of launching an invasion against Morrowind early in the fourth era, seems like they didn't suffer too much during the Oblivion crises. I would imagine the terrain and race of Black Marsh makes it pretty well suited to a guerilla warfare type deal, I could see that giving the daedra hell.