Oyster cards are "smart" cards that you load up with credit and travel on them. it's much cheaper to pay by Oyster than cash if using the London Underground and buses. You pay an initial £3 fee for the card.

Travelcards are a ticket that lasts for a day/number of days. I think it would work out expensive to get a 7 day standard travelcard, but you can get 3-day off peak ones which might be better... I guess it depends on where you're planning on going. Personally i quite like walking round London rather than getting public transport but it's not always an option.

Take a look at TFL Website which should show you various options depending on your plans.