The route we used to climb Mt. Oklahoma in most respects followed the route described by G&M and is also written up in the Roach's book on the high 13ers. The only point of variation will likely be how far up the trail to the North Halfmoon Lakes one should go before turning off the trail to begin the main ascent to Oklahoma.
From the trailhead where North Halfmoon Creek comes in, head north on the old roadbed, which after a while will become trail. For the next two miles, the trail will gain only modest elevation, about 600 feet. At these coordinates, one of the trails to Mt. Massive turns off: N 39° 10' 04.68 W106° 28' 46.03". Do not turn up that trail. Continue west on the North Halfmoon Trail which after the previous coordinates, will pass through another area of forest and then break out into another meadow. At these coordinates, the trail begins to depart the main drainage and gain some altitude. (N 39° 10' 08.60" W106° 29' 05.33" - elev. 11,440 ft.) Follow the trial on up to just short of 12,000 ft. elevation, then depart at these coordinates: N 39° 10' 28.83" W106° 29' 18.08".
Depart the trail and walk westward along an open bench with trees & some willows. Cross a smaller tributary stream and continue walking WSW now through more open trees and low willows to cross a major tributary stream. To cross this stream, you'll need to lose about 150 feet in elevation. Once across, continue WSW following along the edge of another area of trees,, cross a rocky area and as you do, you'll be well below the cliffs on the east ridge of Oklahoma. After passing the rocky area, watch for a small drainage coming down from the west. Head up along that drainage on its south side and hike into a flatter basin. Walk to the west end of the basin using as much tundra as you can. somewhere between 12,600 and 12,700 feet, turn north to gain Oklahoma's east ridge. This will be the steepest part of the hike and will be on mostly low tundra with loose, small, pebbly rocks and moderately good footing to gain the ridge. Once on the ridge at about 13,150 ft., hike NW on spotty tundra, embedded rock and rubble to the rocky summit. Mt. Massive, seen to the east, will seemingly dwarf this summit. For the return hike, go back as you came. Done early enough in the season, you can find some snow fields that may offer some nice glissading. Take and ice axe then.
It is possible to make the long trek from Mt. Massive to Mt. Oklahoma, by following a very long, connecting ridge that forms a semi-circle around the headwaters of North Halfmoon Creek. The main difficulty will come at the low point saddle north of the Oklahoma summit. Crossing that saddle are several rocky ribs that transect the ridge line. Avoiding them entirely would mean losing a fair amount of elevation on the west side. Staying on the ridge means crossing the multiple ribs. This involves some slower, 3rd class scrambling work, but can be done and kept at that level. Beyond that saddle, it's back to Class 2+ boulder & rock hopping to the Oklahoma summit.
Links to other information, routes & trip reports for this peak that may be helpful.