The 27-year-old, dubbed Shrek by his friends, carded a second-round 67 to add to his opening 65 and move to 12 under and a five-shot clubhouse lead over Mark Calcavecchia, and with every violent gust that buffeted the Fife coastline his advantage looked more impregnable.
Officials said enough was enough and 65 minutes was lost when play was suspended due to the winds clocked at over 40mph, and when the hooter sounded for the resumption, overnight leader McIlroy and three-times champion Woods immediately suffered.
Phil Mickelson (71) was sweating over his cut prospects on level-par 144 after being unsettled by the gusts.
"With winds this strong ... your putts from three feet are greatly affected, not to mention trying to make eight, 10 or 12 footers from crosswinds," the world number two told reporters.
McIlroy, who had sat frustratedly on the fourth fairway during the hiatus, resumed with a bogey and followed it with a second dropped shot at the sixth and another at the seventh to fall back to minus six, one behind 1989 champion Calcavecchia.
Woods' resumption -- again greeted by warm applause from the packed galleries -- was just as bad, opening bogey-bogey after he had barely reached the first green when play stopped before getting one shot back at the fifth to go four under.
The driving winds that forced the suspension gathered strength and the heavy morning cloudbursts that forced players to change clothing as often as their clubs were blown away.
Organisers called a halt to the action, and players at the far reaches of the course were left to their own devices during the respite as the Royal and Ancient opted against an evacuation of the links course.
Earlier Oosthuizen, who has played three Opens and missed the cut every time, fired three straight birdies from the fifth to overtake McIlroy's overnight lead of nine under.
He birdied the 10th too before a three-putt from 60 feet on the par-three 11th knocked him back.
Oosthuizen put a chip at the 12th stone dead for another birdie. He then bogeyed the 13th before picking up another stroke at the 14th and capping off a fine round by calmly rolling in from 15 feet on the last for his seventh birdie.
Oosthuizen's best of the day 67 was matched by Calcavecchia, Spain's Miguel Angel Jimenez and American Rickie Fowler.
Calcavecchia, the first to tee off on Friday and playing under the watchful eye of his caddie wife Brenda, posted a bogey-free round which revived memories of his only major triumph at Troon, to finish seven under.
Jimenez lipped out with a putt at 18 that would have been his ninth birdie of the day and had to settle for five under for the day and for the tournament.
England's Lee Westwood and Paul Casey finished on six under, a shot behind Calcavecchia, after contrasting rounds.
Leading completed second round scores (US unless stated): 132: Louis Oosthuizen (SA, 65, 67). 137: Mark Calcavecchia (70, 67). 138: Paul Casey (Bri, 69, 69), Lee Westwood (Bri, 67, 71). 139: Tom Lehman (71, 68); Ricky Barnes (68, 71); Peter Hanson (Swe, 66, 73), Miguel Angel Jimenez (Esp, 72, 67), Graeme McDowell (Bri, 71, 68), Retief Goosen (SA, 69, 70). 140: Ignacio Garrido (Esp, 69, 71); Toru Taniguchi (Jap, 70, 70); Robert Karlsson (Swe, 69, 71), Martin Kaymer (Ger, 69, 71). 141: Shane Lowry (Ire, 68, 73); Vijay Singh (Fiji, 68, 73); Yang Yong-eun (Kor, 67, 74); Dustin Johnson (69, 72).