Will be in Cambridge for a week in August. Will be making at least four trips to London and one to Brighton. Haven't been to UK since 2006. Any recommendations as far as Oyster card? Is there an equivalent for the British rail system? thanks for any help.
Cambridge is well beyond the travel zones covered by an Oyster card so the card by itself is of no use for that trip. The special offer to which Steve refers allows someone with an Oyster card to use a special National Rail voucher to get a super cheap fare from London to Cambridge. The Oyster card itself cannot be used on the train. However, the offer began in June and will expire on 25 July. Too late for you.
The BritRail London Plus Pass would work for you. Read about it here.
Compare the cost of the pass to the cost of an off peak same day return (roundtrip) ticket: £15.80 for NX East Anglia trains only for Cambridge-London-Cambridge. £34 for an off peak same day return ticket or £51 for an anytime same day return ticket for Cambridge-Brighton-Cambridge.
Cambridge and Brighton are way beyond the Oyster area. The tickets are fairly cheap so it probably won't be worth getting advance discount fares given the hassle of being tied to specific trains.
Have a look at this site it will help you sort out the ticket structure in the South East. Also see the 2 for 1 entry ticket offers in London.