I'm looking at going out an buying some Warhammer Invasion this weekend. Do multiples of cards come with each expansion, or will I have to buy the same expansion two or three times to get 3 of the card a need and thus stay competitive?

Somewhere in between. The Core Set and Assualt on Ulthuan comes with cards x1, x2, and x3. Each of the Battle Pack supplements comes with cards x1 and x3 (ten of each type for 20 new cards in a box of 40 cards total).

At this point I'g get the Core Set x1 and Assualt on Ulthuan x1, and each BP x2. That will give you the most diversity to choose from when building your decks without having to buy everything x3. After the Corruption Cycle plays out all future BP's will be all cards x3.