Current strength is number of cohorts, manpower, and gold reserves of your country compared to the defending country. The effect of gold appears to be capped, and manpower is calculated not only by total manpower, but also by what percentage of your total you have left (so only having 20% of your manpower lowers your current strength by quite a bit even if that's still double the manpower of the other country). I think cohort strength is divided by the number of cohorts of the defending country, but I'm uncertain about this. All I can tell is that building huge amounts of cohorts doesn't increase this number by very much. It's not capped though.
Potential strength is the same calculation as above, but instead includes alliance members, defensive alliance members, and any countries that are guaranteeing the defending country. Very importantly, if you guarantee the country, the strength of your country is added to the potential strength of the defending country.
None of this is exact, but from playing, this is what I've figured out. I haven't been able to discern an effect from ships.