The world's two top-ranked players were unable to fight back after disappointing first rounds and carded 73 and 72 to end 10 over and 11 over respectively.
McIlroy said: "It's just such a demanding golf course and punishes the slightest shot that's off-line or that's maybe not the right distance."
Five-time runner-up Phil Mickelson took 71 to end seven over, but Masters champion Bubba Watson also fell foul of the eight over cut mark with 78, 71 for nine over.
The 36-year-old Woods, three shots adrift of leader Michael Thompson in tied second overnight, picked up a shot at the third to take the lead but went backwards with three straight bogeys from the fifth.
But he settled himself with two pars before further birdies came at 10 and 13, and he missed other decent chances, notably on the 17th.
"It was really, really tough and I just had to stay as patient as possible," said Woods.
"I think I'm in a good spot. This tournament, you just keep plodding along.
Andrew CotterBBC golf commentator at Olympic
The kind of players near the top of the leaderboard show exactly what type of game it takes to win a US Open. There's Tiger Woods, of course, who continues to hit more fairways than almost anybody here, 11 of 14 on day two with 14 of 18 greens in regulation. But also Furyk, Toms and McDowell who are all shorter but deadly accurate players, great putters and very patient grinders. And the fact those three are all major champions will certainly give Woods pause for thought. They're unlikely to be intimidated by him and a fascinating weekend lies ahead.
"You're just playing for a lot of pars. This is not a tournament where we have to make a bunch of birdies."
Woods's last major triumph came at the 2008 US Open before turmoil in his private life, injury and changing to a new coach derailed his progress. But eight times out of nine when he has held at least a share of the lead after 36 holes at a major he has gone on to win.
"It's been a very long time since my swing felt this good - don't forget I went through all of last year hurt and hadn't been able to practise," he added.
"Now it's becoming more consistent, day-in and day-out."
Furyk, who won his solitary major at Olympia Fields nine years ago, mixed two birdies with two bogeys to edge into contention.
"I kept the ball in the fairway pretty well," said Furyk. "I feel solid and in control so far. I know it's going to get even firmer and faster and even more of a stern test for the weekend."
Disappointed McIlroy on US Open exit
The 45-year-old, who also has four other top-five finishes in the US Open, said of the typically tough set-ups: "I guess you have to realise at the US Open that par is a really good score and you're going to make some bogeys.
"Mentally you have to be in a good frame of mind, and physically you have to be on top of a lot of areas of your game."
Toms joined the leaders late on with two bogeys on his front nine and two birdies on his back nine.
"I just hung in there," said Toms, who beat Mickelson for his US PGA title in Atlanta. "I knew not to get frustrated and keep grinding. You have to be mentally ready for anything and never give up."
England's Justin Rose followed his opening 69 with a 75 for four over alongside Ireland's three-time major champion Padraig Harrington (70).
World number three Lee Westwood (72), fellow Englishman Ian Poulter (75) and Scotsman Marc Warren (72) ended five over.
Seventeen-year-old amateur Beau Hossler led on his own briefly before falling back with a 73 to end three over, while 14-year-old Andy Zhang carded 79, 78 for 17 over.
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