While we're talking about Ragnar, I'm playing as him now. Great exploit potential on maps with naval combat:
1. Get metal techs and resources and spam swords and axes early and get some promotions on them using Barbs, buildings, theocracy, wonders, seeded generals, etc. Spamming them for several reasons, including keeping strong enought to avoid an unwanted early DoW. Use your little army if you need, but protect it and your cities mostly. Don't waste too much time with Spears, Archers and Horses, though you'll want a few to have a good mix.
2. When you get Berserkers, promote these guys and they are now Amphibious! Same rule on not throwing away these troups in an early fight. If you've got to fight or the odds are excellent against a weak neighbor, then go for it. But you are building this army for the future. Be sure to build a few Trebs in case you need them in case of an early DoW.
3. Get to Rifles as quickly as you can. Don't waste time building Musketmen while you are on the way. Keep building Berserkers, expecially in your HE city while you are researching up to Rifles.
4. When you get to Rifles, you can promote those Berserkers to Rifles AND THEY KEEP THE AMPHIBIOUS TRAIT! You suddenly have primitive Marines and if you did a good job getting Rifles early, you'll have a tactical edge.
5. Continue researching useful techs, but build your cash. A GM for a few grand could be real useful around this time. Keep building Berserkers in your HE city. You can also draft non-Amphibious rifles as much as you want in your Globe city. Make sure those aren't the same city because the uses don't really overlap well.
6. Avoid getting the techs for Grenadiers as long as you reasonably can. Once you get them, you can't build any more Berserkers.
7. Once you are ready to advance further down the tech path, make Steel a priority for upgrading your Trebs to Cannons. You may want to consider a few quick Cannon builds in your HE city. Next priority is Assembly Line, for the promotion of all these Rifles to Infantry.
Anytime between steps 3 and 7, you can start initiating war plans taking advantage of your Amphibious traits. There are two important ways to take advantage of it:
A) Obviously, you can load them on ships and take out cities with them. You may want to have some Frigates along to reduce defenses, but if you are playing with a strong tech edge, well-promoted rifles should be able to take most cities held by anything less than Grenadiers without much trouble. Some cities will be on other continents or islands and couldn't otherwise be taken at this time, except by offloading any old troops on the shore, which loses the element of surprise. This is also good for going after the coasts of nearby opponents. Amphibious city attacks that are well-planned can take out large numbers of coastal cities without the AI getting a chance to counter attack. You can often get an early capitulation with such a strategy. They same troops without Amphibious could attack those coastal cities from the land side with the same odds, but they couldn't do it as quickly.
B) Across lands with lots of rivers. This is a more limited but potentially important strategy. If your opponent's city is beside a river, station your stack with lots of Amphibious Rifles across the river, preferably on a forested hill. If he attacks out of the city, for instance with cannons, his odds will be worse because of the river. But you will have no disadvantage for your Amphibious troops and your Cannons and Trebs will do fine on Bombarding defenses.
Love to see a full discussion of Ragnar here.