I heard the expression Adam and Eve on a raft for the first time today when listening to the repeat of 'the antidote to panel games' I'm Sorry I Haven't a Clue (available here for another week). It was part of a very silly round devoted to egg-related questions (about 20 mins in). And, indeed, Adam and Eve on a raft is American diner lingo for 'poached eggs on toast'.
Adam and Eve on a raft is in the Oxford English Dictionary, marked as US slang. The first citation dates back to 1894:
1894 North-eastern Daily Gaz. (Middlesbrough) 15 Oct., One day he ordered poached eggs on toast. Going to the slide the waiter yelled out: ‘Adam and Eve on a raft.’ The order was changed to scrambled eggs, when the waiter rushed off, and in stentorian tones there came the alarming direction to those below: ‘Shipwreck that order!’
There is an earlier citation in the OED (from 1891) where Adam and Eve (without a raft!) means 'ham and eggs'.
The term Adam and Eve on a raft is not used in the UK. Adam and Eve here is Cockney rhyming slang for 'believe', usually heard in the question "Would you Adam and Eve it?"