Cueto's quick-fire treble came in the space of just 12 first-half minutes as England felled the Mighty Oaks in comprehensive fashion.
Ashton added two more before the interval as England pocketed the bonus point inside 31 minutes.
The Northampton wing then completed his own hat-trick in the second half after Ben Youngs, Ben Foden, Manu Tuilagi and Tom Croft had all joined in on the try-scoring action.
If Argentina fail to beat Scotland tomorrow, England's qualification for the World Cup quarter-finals will be confirmed.
Cueto, who was starting his first match of the tournament after recovering from a back injury, had scored just one try in his previous 25 Test appearances.
But the Sale wing came roaring back into form to run in his second Test hat-trick, and the third by an England player at the World Cup. Ashton then became the fourth England man to complete a World Cup treble.
Cueto was back in England colours along with Mike Tindall as Martin Johnson fielded his strongest available side against the Romanian second string.
The eastern Europeans prioritised Wednesday's game against Georgia and once England found their rhythm the match became little more than an opposed training run.
England laid waste to the Romanian line-out, Tuilagi was prominent in midfield while captain Lewis Moody and number eight James Haskell both enjoyed strong games.
There will still be elements that will concern Johnson, notably the needless penalties England conceded which undermined an otherwise bright start.
Johnson had blasted his men for being "sloppy" against Georgia last week - but England did eventually find the ruthless edge he demanded.
Jonny Wilkinson kicked England into a second-minute lead after a strong carry from Louis Deacon and then built the pressure again after a scruffy Romanian line-out.
Foden's pass to Ashton was judged forward when a try was in the offing - but England did not have to wait long to make their breakthrough.
Wilkinson's long pass found Ashton, who fended off the defender before drawing the last man and sending Cueto clear on the overlap.
England were playing at pace and had found their precision.
Youngs took a quick penalty as England moved to within five metres and the ball was swung wide for Cueto, who dummied to cruise over for his second.
England had Romania on the ropes and Cueto completed his hat-trick inside 12 minutes after finishing a clinical counter-attack, which began with Tindall winning a turnover in his own half.
England secured the four-try bonus point when Ashton finished a classic training-ground move, collecting the inside pass from Wilkinson after Croft had won clean line-out ball.
Ashton then streaked away for his second try three minutes later after excellent work from Deacon and Steve Thompson, who both drew defenders to create the space.
Romania got themselves on the scoreboard with a penalty from Marin Danut Dumbrava just before the interval.
England replaced Wilkinson with Toby Flood and Dan Cole with David Wilson at half-time - and carried on where they had left off with a try after just 20 seconds.
Youngs launched the attack with a break down the blindside deep in England's half and he combined with Tuilagi before receiving the pass back to score his second try of the tournament.
Foden scorched over for England's seventh try after Tuilagi had burst onto a flat pass from Flood and broken through the Romanian line.
Romania enjoyed their best passage of play just before the hour mark, after Tom Palmer had been penalised for failing to release and the Oaks went for the corner.
Romania's strength lies up front, as Scotland almost found to their cost in the opening game, and England's defensive line had to repel wave after wave of pressure.
But England cleared their lines and then hit the half-century through Tuilagi, who stormed through a gap to score his fourth try in five Tests.
Tuilagi and Cueto combined to send Croft over in the corner before Ashton wrapped up his hat-trick with England's 10th touchdown of the day.
Palmer sparked the move with a deft offload, Haskell rampaged upfield and Ashton streaked away to score in the corner.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.