Unorthodox spinner Mendis played a key role in his team's stunning 55-run victory over South Africa in a rain-hit match at Centurion on Tuesday, grabbing three wickets for 30 runs.
"We have not played Mendis and some of their seam bowlers before," said Strauss, whose team were beaten 6-1 in a recent home one-day series against defending champions Australia.
"Everyone will have his own game-plan against him (Mendis). You can look at a lot of footage of him, but it is only in the middle that you can be really sure of how he bowls and what his variations are.
"It requires us to think pretty quick on our feet. There are some fundamentals you have to keep in mind against someone like him, but it is a new challenge."
Off-spinner Muralitharan, the world's leading wicket-taker in both Tests and one-dayers, and paceman Lasith Malinga, with his slinging action, are the other bowlers who could keep pressure on England.
"They ask different questions of you. It's only by facing them you can be sure of your game-plan. We have played against Murali and Malinga, but Mendis is new."The way he (Mendis) bowls makes life difficult for batsmen, but to an extent the pace he bowls at provides opportunities for batsmen as well once you get used to his variations.
"Sri Lanka are a good side with a lot of confidence. It will be quite exciting to play against them."
Strauss conceded that England's one-day form had been a cause of concern for many years.
"The one-dayers have been an ongoing concern for a number of years. The players are really excited about moving forward as a group. It will take a bit of time to happen," said Strauss.
"In the meantime, I maintain we are capable of beating anyone but we haven't had the consistency over the years. A change in environment can make a big difference. We have to start looking forward.
"There is something quite exciting about world events. It's quite exciting to know if you play well in three games you're in the semi-final."
England are without match-winners Kevin Pietersen and Andrew Flintoff, who are recovering from injuries.
"Freddie and KP are two of our best one-day cricketers. But Freddie has been out quite a lot recently and we are used to that and we've got to move on," said Strauss.
"It's also a chance for other guys to step up and make a name for themselves."
South Africa and New Zealand are the other teams in Group B, with the top two sides advancing to the semi-finals.
England (from): Andrew Strauss (capt), James Anderson, Ravi Bopara, Tim Bresnan, Stuart Broad, Paul Collingwood, Joe Denly, Eoin Morgan, Graham Onions, Matt Prior, Adil Rashid, Owais Shah, Ryan Sidebottom, Graeme Swann, Luke Wright.
Sri Lanka (from): Kumar Sangakkara (capt), Sanath Jayasuriya, Tillakaratne Dilshan, Upul Tharanga, Mahela Jayawardene, Thilan Samaraweera, Chamara Kapugedara, Angelo Mathews, Muttiah Muralitharan, Ajantha Mendis, Thilan Thushara, Nuwan Kulasekara, Dhammika Prasad, Lasith Malinga, Thilina Kandamby.
Umpires: Aleem Dar (PAK) and Billy Bowden (NZL)
TV umpire: Tony Hill (NZL)
Match referee: Javagal Srinath (IND)