First off, a lot of great advice here, and I'll add my two cents to the thread. Mid and short irons and wedges have to be solid on Oakmont, or you will be constantly looking at really difficult two putts. I leave the hybrid at the clubhouse and use 3 wedges - 54, 60 and 64. Or if you love your hybrid, leave the 3W behind IF you have a 270+ driver and an iron set with a 210+ 3 iron. With that equipment setup there are only 3 holes you will use the 3W - the 2nd on the two par 5's and the tee shot on 17. A 3 iron with topspin will still leave an easy approach on all 3 holes. The three wedges give you all the options from 100 yards in to get close on punches, flops, pitches, and chips, which can save many of those putting headaches. You also have to think your way around this course. Attack the holes where birdie is possible, and play for par on the holes where being aggressive and missing will cost you dearly. This isn't like Kiawah where you just take aim and let it go. This may seem really elementary, but limit your bogeys here and you can post a qualifying score once you figure out:
The Greens
Somebody posted a putting tip on June 1st or 2nd that is solid gold, and holds true for both Oakmont and St. Andy's. The tourney speed is right on 70% of the distance (length +/- elevation). Reprased, take the distance with the flag at the hole, add or subtract the elevation, and multiply by .70. For example, an 8 foot, 2" uphill putt should be hit 7+ feet, Yup, I keep a calculator at the ready and use it frequently to figure out putting distances. Sounds rather geeky but it works - I just posted a 64 with 27 putts, and my average distance after my approach was 14 feet. On the uphill putts give them a little extra juice, as the ball just dies at the hole on several greens when you are putting uphill. On the short putts with break, go at them aggressively to take much of the break out of the equation. You'll make far more this way than you will miss.
On those nasty breaking putts (like being left of the hole on #9), I use the calculation at the hole to set the distance. For instance, a common putt there is say maybe 32 feet, down two inches. Then set the marker for the break. You might have something now like 34 feet, uphill 3". But, use the original and hit a 21 foot putt (32' - 2" x.7 = 21 feet). This will take off a lot of that downhill speed as the putt breaks, and should leave a very makeable 2nd putt (using the distance calculation from where you set the marker is how you end up 20 feet below the hole and a near certain 3 putt or more). Also, roughly double the amount of break you would apply on the other courses.
My last suggestion is something that has been posted in the past and is very handy on every course but especially at Oakmont, and I'm sure many use this method. I have the Redwood putter, and will frequently "club up". Have a 30' putt? Use the 150' meter and pull back two increments. 25' putt? The 90 foot meter two increments. 12 foot putt? The 90 foot meter one increment, and so forth. This gets the ball moving quickly and takes out some break. I rarely use the suggested meter unless the putt is less than 3 feet. Search putting tips in the forums and you'll find lots of information on this technique.
Hope this helps, and good luck taming the Beast. Many will say all of that is way too complicated, just give us some greens we can putt on! But for me all this works, and my Oakmont 3 putts are now nearly extinct.