At tea, England were 123 for one -- a deficit of 247 runs after West Indies had made 370 in their first innings.
Strauss was 45 not out and Jonathan Trott 35 not out, with their unbroken second-wicket stand of 80 coming in just 101 balls.
Alastair Cook, Strauss's fellow left-handed opener, was the man out in the session, for 24, after twice being 'caught' behind off no-balls.
Fast bowler Kemar Roach repeatedly over-stepped -- his 10 overs had so far featured eight no-balls.
One of those was when Cook, whose 79 helped England to a five-wicket win at Lord's that gave England a 1-0 lead in this three-match series, was brilliantly caught one-handed by diving wicket-keeper Denesh Ramdin for one.
However, Cook was recalled after umpire Aleem Dar used television technology to check for a no-ball he hadn't called on the field.
It was a similar story when the paceman, angling the ball had Cook, on 12, edging a regulation catch to Ramdin.
This time, however, Dar had signalled the no-ball himself.
But Cook wasn't able to make the most of his double reprieve.
Ravi Rampaul, who missed the first Test with a neck injury, produced an excellent rising delivery which Cook could only nick to the reliable Ramdin, who made no mistake as he 'caught' the Essex batsman for the third time.
Rampaul kept things tight in an opening spell of one for 28 in 11 overs.
But the pitch was still a good one on which to bat.
Strauss's back-foot force for four off Sammy brought up England's fifty while Trott got off the mark with a cover-driven boundary against the medium-pacer.
Eventually, with England 96 for one, Sammy brought on Shane Shillingford after the off-spinner had been left out at Lord's.
It wasn't long though before Trott was driving him for four while Strauss weighed in with a trademark squre-cut four off Sammy, whose pace meant he'd little margin for error on such a good surface.
West Indies resumed Saturday on 304 for six, having collapsed to 63 for four after their top-order's latest failure, with Marlon Samuels 107 not out and all-rounder Sammy a then Test-best 88 not out.
Sammy went to 98 by slicing a drive off Stuart Broad over the slips and next ball had another lucky break when, aiming legside, he somehow got the ball through point for another boundary that took him to a century.
But the 28-year-old, playing his 26th Test, had produced plenty of 'proper' shots too in completing a 140 ball-hundred with a six and 16 fours in just over three hours at the crease.
However, both he and Samuels were out soon afterwards as Tim Bresnan, expensive on Friday, removed the century-makers in a spell of three wickets for 10 runs in 19 balls that saw him finish with four for 104 in 27 overs.
Sammy was dismissed when he holed out on the hook to Kevin Pietersen at deep square leg.
His partnership of 204 with Samuels was a West Indies record for the seventh wicket against England, surpassing the 155 shared by Garry Sobers and Bernard Julien at Lord's in 1973.
And 340 for seven became 341 for eight when Samuels, who'd added just 10 to his overnight score, edged Bresnan and Anderson held a sharp catch in the gully. (
