Well, it's been hard to get a really good feel from fighting just the AI because it's not very good with several of the nations. But I will give my best assessment. I don't think I know enough to rate them from 1 to 7, but I will group them into close proximity.
Top tier nations: Orcs, Insects, Jomon.
Orcs - The orcs have a stronger start than the insects (I think, I haven't played a new orc game yet since the last update) and should expand faster, plus they don't need to worry about resources so they can build as many forts as they can afford to build from (advantage over normal nations). They can either build straight heroes for early power or build mages also to get access to their better units. They did lose some armor in the most recent update but that shouldn't make indies too much harder I think. They're still decent in melee so most races will have a fair fight trying to fight off their numbers. As long as they don't lose too many commanders early on they'll just get stronger and stronger as the game goes on. If the game lasts too long though I think nations with strong magic will probably have the advantage, I still have yet to summon anything with the orcs yet so I'm not sure how strong they'll be, but chances are anything that will kill a normal army of orcs will probably kill their summons too.
Insectoids - Don't expand as fast as the orcs, but don't have to. All they need is population. Since you can't make queens in space they only care about planet provinces. They start off fairly slowly, but they are *very* good fighters and if they aren't exterminated early will grow to have huge amounts of troops. Pretty much the only things that can melee them effectively are jomon's suits, but they can't make nearly as many. The insects really come into their own in about year 3, by that time they should be able to kill basically anyone 1 on 1, except MAYBE the orcs. The insects are also stronger late game than the orcs, because they take a lot less damage from aoe and they should be able to spare males for suicidal dashes into enemy ranged blocks. Followed by massed dreadnaughts. I'm not sure if anyone could really deal with that.
Jomon - Massable, high damage armor negating ranged weapons, some of the best melee units in the game, dai oni, and aka oni. The ice battle suit samurai are less massable than insectoid armies, BUT they are also very hard to hurt with ranged weapons, so they are very solid units. Plus paralyze damage on their staves means they are a good counter to thugs/scs. Their dai oni are fairly powerful as mages and scs, though you have to craft gear for them as they have only fist as a melee weapon right now. But properly equipped they should be able to kill most other things in melee, and solo armies. They don't quite have ulm's magic diversity and their recruit-everywhere mages aren't as good but jomon also doesn't need magic as much. Especially since aka oni will do a pretty good job of decimating human-sized units. Aka-oni are probably only too strong against ulm and the commonwealth, orcs might be able to deal with them but it would be hard if they were massed enough. Jomon's wraith suit shinobi are also some of the better assassins. And Jomon has some of the best units in space. They aren't as overwhelmingly powerful at any stage as the orcs or insectoids can be I don't think (except on commonwealth/ulm with aka-oni) but they're also less vulnerable to the above nations and should be strong the entire game.
Mid tier nations: Commonwealth, Ulm.
Commonwealth - The commonwealth doesn't have terribly effective ranged units for the most part, but they have the best shields in the game and are basically invulnerable to non-aoe ranged attacks. They also all have magical weapons. They're pretty strong in melee but not ridiculously so. They'll tend to win pound for pound against most melee units but they're fairly resource-intensive so they won't have huge numbers of troops. They also have to fight in cold provinces or they are much weaker. They have very powerful water magic but not a whole lot else, so they are somewhat magic-limited. The commonwealth seems to be a lot better defensively than offensively due to their turrets and cold weather abilities. I could see them being pretty tough to dislodge but they would conquer other players fairly slowly.
Ulm - Ulm has the most magic diversity, a good selection of troops, recruitable SCs, powerful summons and is terrible in space until late game. Ulm is another fairly defensive race in that they are just so much better on planets than in space. Their marines and black knights are capable but in space most things will beat them given similar resources. On land they can add artillery marines which are good if not as good as aka-oni, or tanks if they want something hardier. Before battlefield damaging spells come into play though the artillery marines are probably much more efficient as tanks are pretty expensive and relatively easy to kill in melee. Ulm though can get lots of artillery and buffing mages, and should have massive amounts of earth gems to use for crafting, globals and summons. Ulm has the ability to kill just about anything given the right troops at the right time, but will struggle against jomon, insectoids and orcs. Ulm is decent early, fair towards the middle game and really comes into its own in the end game. Ulm is a very good case for casting Riches from Beneath and Earthblood Deep Well.
Low tier nations: Dragons(?), R'lyeh.
Dragons - I'm not sure whether Dragons belong here or with mid-tier, as I have not played as the dragons since they were incorporated, only against them. But since they are so expensive and relatively vulnerable to ranged attacks, they will probably be fairly weak until they get some research done and can forge/summon. With the dragons that can take a long time due to how expensive research is for them. On the other hand massed bonebiters are still strong, and can reach the enemy in one round. This is still bad for pitched battles, but the dragons would make great raiders. They will probably have to raid with small groups of dragons while building up research to turn out thugs/scs. The dragons do have probably the best recruitable assassin in the game, especially early, which could help a lot. If the dragons can survive until they get their late game research they should be able to kill everyone, everywhere.
R'lyeh - R'lyeh is, in my mind, almost certainly the weakest nation (but then I'm not very good with MA R'lyeh either, which is what they remind me of). They do have some things going for them. They have lots of magic, which they can do the usual illithidy things with. Covering astral, water, earth and death fairly well. However they don't get nature, which combined with them not being secluded from most other races makes the R'lyeh clamming turtle strategy a lot harder than in vanilla. Also, most of their recruitable units are both expensive and not very good. R'lyeh can expand fairly quickly but once their slave troops don't fare very well against most national units and then they just have illithids, sitting there getting shot. Pirate raiders are probably their best bet for protecting the swarm of illithids that is actually going to kill the enemy. Unfortunately said swarm of illithids is pretty expensive and will make it very difficult for the player to do much in the way of research. R'lyeh could try to get around this by not building armies until they're being attacked but that's probably not the best idea. If they survive until mid game they will start becoming more viable but I think they would have a hard time killing anyone until then. If they survive until late game they'll be pretty dangerous, especially as they probably are one of the best sc killers, but their pretty bad early game would make things hard on them.
Whew, that was long! Anyway, those are just my observations from my own play style and understanding, and obviously the latest update changed things a bit so I don't know entirely that some of what I said is correct. Feel free to disagree where you will