It was another disappointment for Strauss who has failed to score a half century in his last 15 test innings.
Alastair Cook finished the day at 12 not out after what appeared to be a good appeal for caught behind off Corey Collymore. Captain Michael Vaughan was with him on 10.
England had started the day brightly by adding 74 to their overnight total.
Ian Bell was caught behind off Collymore just three runs short of his seventh test century. Sidebottom and Panesar then added an entertaining 32 runs to leave them with 370 for the first innings.
Only three overs were possible before lunch during which West Indies lost stand-in captain Daren Ganga lbw to Steve Harmison.
Harmison struggled with his line all day and though he occasionally showed evidence of the form which brought him 11 wickets against Pakistan at Old Trafford last year he was often erratic
Shivnarine Chanderpaul, top scored for West Indies with 50 in an innings where the next best total came from 42 extras.
Aggression and intent
At tea West Indies were on 153 for three but Panesar said advice from Peter Moores, the England coach, and new bowling adviser Allan Donald, the former South Africa pace bowler, changed the course of the game.
"They said we should show more aggression and intent and we did that as a unit," Panesar said. "It's important to bowl in the areas you want to get them in."
Panesar struck seven balls after tea dismissing Devon Smith to put West Indies on 157 for four. It was the left-arm spinner's 50th test victim.
The collapse continued as Sidebottom and Panesar wrapped up the last six wickets in just 44 balls. The West Indies innings had lasted just 52.4 overs.
West Indies coach David Moore was left frustrated by his batsmen.
"I am very disappointed," the Australian said. "We went from a very good position at tea to a very poor position. I expected us to bat for the day but the batters didn't back up the bowlers."