It's
very helpful to involve another civ. The enemy then fights on 2 fronts, and that's never a good thing. Sometimes you don't want a strong civ to help, because you might just build a monster. Watch out for that. I wouldn't invite Rome to the party for that reason.
You're building an army with 4 cities. That would only take about 10 turns before you knock on the first city's door.
I wouldn't go after Rome first - since they are the bigger one. I'd make myself stronger by attacking Russia (sounds counter-intuitive, but if you attack them, you grow your army in those turns, gain Iron and land.)
Rome might even run into the Scandinavians while you're battling Russia. That would be a bonus.
If that would happen, maybe you can join the war vs the Scandinavians, get a few bucks from Rome for doing absolutely nothing in the process, making sure that war rages on while you build your war machine behind the Roman backs.
I'd do Russia first and just get rid of them altogether - maybe Yakutsk will be hard to reach... I'd build Javelin throwers first,
then catapults because the Javelin throwers reduce unhappiness while you wait for the cats to finish. (not the other way around what you're doing now)
Take Russia, enter Golden Age after your first successful battle. Also, your Javelin throwers enslave beaten enemies turning them into Slaves and remember: Slaves require No Upkeep

Hooray for Slaves!! This means you can cultivate your newly conquered land (Russia) very quickly and you can road the Incense and Iron into your land! Those are big advantages.
If Russia had Iron all the time, expect a nasty bunch of 3.2.1 Swordsmen on the counter attack. Run to the hills and make sure you defend with cats a lot.
Then with 3 civs left on the continent, I'd go after Rome with just a little help from my Northern friends.
Asking Rome to help vs the Russians is not unnecessary and costly and might hurt you in the long run if Rome becomes too powerful - and what are they going to do anyway? Attack Yaroslavl? You don't want that.
What would be hilarious though, is to make peace with the Russians before you take their second to last city. Ask for Yakutsk as payment for peace. Then take out their last city the next turn. Give Yakutsk to the Scandinavians.
(oh and if you wonder if you can ever get that Warrior back? I think you can. Border hop him towards your land. Make him stand on one side of the Rome/Scandinavian border in one turn and on the other side the other turn)