A regular Oyster card requires a £5 deposit which is refundable if you hand the card back. It has to be bought in London or ordered to a UK residential address.
A visitor Oyster card can be bought in various locations outside London or delivered internationally. There is a £3 non-refundable charge (plus delivery if applicable).
Both cards give access to the same fares for single trips and day passes. Regular Oyster cards can be registered and have a photo attached to them, which makes them usable for weekly passes and up.
The fare difference between paper tickets and Oyster is currently £2.50 for a ticket through central London (Zone 1). Even a visitor card saves money if you make more than one trip during your visit, provided that you get a refund for any unused credit. The only reason to use a paper ticket would be if you're in a hurry when you leave London, or leave via a route that doesn't take you past a station where you can get a refund.
You can get a refund for the remaining credit and for the deposit on a regular Oyster card (but not for the Visitor card fee) at any ticket office. A major station like Kings Cross St Pancras will have a ticket office open all the time the Underground is running. You will get a refund either in cash or on your credit card, depending on how you paid. Beware that if you used multiple cards, or cards and cash, to top up the card at different times, a station may not be able to refund you — you might need to mail your application to the customer service department, which is not practical for a visitor. So stick to the same card, or stick to cash.
There is a group fare for groups of 10 or more, but only for day tickets, and you always have to travel as a group. The discount is substantial, but for a single trip during the day, it isn't worth it.
The Oyster fare from Kings Cross to Custom House or Prince Regent is currently £3.20 at peak hour and £2.70 off-peak. Peak hours are 6:30–9:30 and 16:00–19:00 weekdays; the time that matters is when you start your trip. As far as I know, the minimum amount of money you can put on an Oyster card when you buy it is £10 (not including the deposit). So you should spend £15/person when you arrive and get a refund of £8.60–9.60/person when you leave. Even with currency conversion fees, I expect this to be cheaper than sinking £3 in a Visitor card.