At tea, England were 197 for one after batting through the second session without losing a wicket.
Strauss was 84 not out, after being dropped before lunch on 43, and England captain Michael Vaughan, who'd won the toss, 57 not out.
The duo's second-wicket partnership was now worth 121.
England resumed after lunch on 115 for one with Strauss on 43 and Vaughan 23 not out.
Left-arm quick Rudra Pratap Singh struggled for control and bowled two huge wides. And when he did get one straight, Vaughan pulled him for four.
Strauss's extra-cover driven four off Shanthakumaran Sreesanth brought up a fifty stand with Vaughan and the left-hander subsequently completed his own half-century in 109 balls with nine fours.
It was his second fifty in as many Tests after he made 77 against West Indies at the Riverside last month.
And when left-arm quick Zaheer Khan strayed, Strauss square-cut him for four - a sure sign he was in form - as England reached 150. Vaughan too was in good touch, leg-glancing experienced leg-spinner Anil Kumble for four.
Star batsman Sachin Tendulkar came on to bowl his occasional leg-spin in a bid to break the stand but met with little success.
Strauss, batting on his Middlesex home ground, was lucky to be at the crease after an uppish square drive went straight to point where Dinesh Karthik, a wicket-keeper by trade but playing a as a specialist batsman, somehow dropped what seemed like a routine chance after apparently failing to sight the ball.
Earlier, Strauss and fellow left-hander Alastair Cook made a brisk start with their fifty partnership up in 52 balls.
India's seamers generally struggled with their line although Strauss did unconvincingly edge through the slips on a couple of occasions early on.
But Cook was quickly into his stride, clipping his first ball, from Sreesanth, off his legs for four.
It was left to former captain Sourav Ganguly, the fourth bowler used, to break the stand.
Better known as a batsman, his good length medium-pace was well-suited to take advantage of the swing on offer and with his fourth ball he had Cook lbw, for 36 off 39 balls with six fours, veteran umpire Steve Bucknor taking his time over the decision.
England were now 76 for one in the 15th over.
Vaughan though drove Ganguly through extra-cover, one of the Yorkshire batsman's signature shots.
England gave a Test debut to 6ft 7in Hampshire quick Chris Tremlett, included after Matthew Hoggard was ruled out with a back problem.
The hosts, who earlier this season beat the West Indies 3-0, were already without injured fast bowlers Stephen Harmison (hernia) and Andrew Flintoff (ankle), both of whom were set to miss the whole of this three-match series.
Brief Score (at tea, D-1):
England 197 for 1 (Strauss 84 n o, Vaughan 57 n o, Cook 36; Ganguly 1 for 24) Vs India.