What's the best way to build a 2v2 Rain Dance Ludicolo?
Modest or Bold? Swift Swim or Rain Dish?
I'm leaning towards Bold with Rain Dish. It'll take hits better, allowing it to put up Rain Dance more often.
The team is slow-paced, with Lapras, Vaporeon, Lanturn, Swampert, Gyarados, and Ludicolo. The idea is to start with Vaporeon and Ludicolo, put up Rain Dance while Vaporeon does whatever, then switch into Lapras, using the Rain boosted Surf to heal one another. Vaporeon Baton Passes into appropriate counters for whatever they send, most notably Lanturn and Swampert for electric attacks with Gyarados and Ludicolo walling grass.
You may want to consider Toxicroak as a possible addition to the team...
It has the ability Dry Skin, which means it heals 1/16th HP per turn in rain, and it functions as Water Absorb, healing itself instead of taking damage from any water attack. Plus, it'll add up a bit of variety to your mono-water team. Unless you really want to have your whole team as Water-Types only, I'd heavily suggest Toxicroak.
Roserade can also work well in Rain Dance. It can learn Weather Ball, and in Rain Dance, it becomes a Base 100 Water type attack, which is very strong. It can also give you more coverage, seeing as you'll be able to effective use very strong Grass attacks, instead of having to rely on your Ludicolo to cause damage.
Roserade can learn Extrasensory (Psychic), Shadowball (Ghost), Leaf Storm (Grass), Sleep Powder (Good Status Inflicter), and a bunch of other sweet moves.
Is there a way to calculate EVs? Or do I just need to get 11 berries for every stat to make sure I wipe out a (traded) pokemon's IVs?
Well, actually, if your Pokemon has no EVs left in the stat, it'll tell you the berry has no effect and won't be used.
You won't need 11 of each berry unless each of your EVs are all 101 or over, which I doubt.
101 x 6 stats = 606 EVs, which is clearly over the 510 EV limit. It's impossible to need 11 x 6 berries = 66 stat reducing berries to clear a single Pokemon.