I shoot T&F, running, triathlon, cycling, etc. With a 1Dx, 5D Mk III and the 70-200 f/2.8 IS, you have more than enough equipment to produce great T&F photos. With the 70-200 Mk II you can shoot all day at f/2.8 and not have issues with blur unless you're talking about situations where you don't have enough DOF for the subject (multiple runners stacked around the corner).
You want a MINIMUM shutter speed of 1/500 unless you're specifically doing panning or other induced motion blur shots. At 1/1000 and above you should never have a problem with blurred T&F photos with respect to motion blur.
So then we're talking about focusing. Either the 1Dx or the 5D Mk III have fantastic AF systems that should allow you to get good focus while tracking moving subjects. My typical setup for T&F type events is Ai Servo, Single Point w/4 pt. expansion, and high speed shooting mode. In some situations I may change to single AF point only, or to AF w/8 expansion points. The cases for those may be counter intuitive if you don't understand the AF system and what you're trying to achieve. What I mean by that is that the instance that I go down to a single point is when I'm shooting a single runner in a group. In that instance, using expansion of either 4 or 8 points, or zone or all 63 pts can confuse the AF system. It's going to find focus on whatever makes the most sense to it, not necessarily the runner I am trying to get sharp focus. So I change it to single point and track the runner with that point. This is important for things like you've posted where you really want the lead runner in focus for sure. The rest can fall out of focus, if that is your intent. If you want them all in focus, you need more DOF (smaller aperture) and more ISO to compensate for the loss of light.
With the 70-200 IS II, properly calibrated on either a full or crop frame, you can track a single runner with the primary AF point high on the chest or head, at f/2.8 and have them come out sharp. The 1Dx will get VERY slightly more of a burst of, say, 8-10 in focus than the 5D Mk III. But the 5D Mk III will shoot most in focus up to filling the buffer.
Very few moving sports lend themselves to single shot AF in my book, unless you are using the back AF button and only shooting a single shot. The problem with that is often that you'll miss the peak moment with your single frame. I get far better take by shooting a burst of 3-5 shots of a runner, using AI Servo AF. Using single shot AF with burst shooting is a non-starter. The AF may hit on the first shot, but will never catch up after that, particularly if the subject is moving toward or away from you.
I shoot these sports with a 1D Mk IV, 5D Mk III, and 7D. The main lenses I use are the 300 f/4 IS, 70-200 f/2.8 IS Mk II, and the 135 f/2. Occasionally I'll use the 100-400 zoom, but only when I can't be down at the field. The 300 f/4 IS can be marginal on the 5D and 7D in anything less than good light and when tracking subjects coming directly at me. In good light on the 1D Mk IV, it is a pretty great piece of gear, though the resulting photographs are just "good event photos" rather than the great images that the f/2.8 version gets when I rent it.
I also heavily use wide angles of 17mm on up to 35mm, either zoom or prime, to shoot these sports. The key is to use them from low angles so that the athletes rise well above the horizon. I call them my "superhero" shots. You can see lots of those in my sports galleries.
My favorite shots come from using either the wide angle superhero lenses or the 135 f/2...ALWAYS at f/2. Head to toe runner shots with the 135 L, with the athlete filling the frame are awesome. I use this lens all the time in tight trail confines in the forest when I'm shooting ultra running. Far better than the 70-200 IS II.
The best things you can do to get great shots, though, have little to do with gear and all to do with your framing and composition. Shoot often from low angles, even with long lenses. For instance, shoot the long jump laying flat on the ground from off the end of the pit, at least 135mm and 200mm is better. Aim up and fill the frame with the athlete, while keeping the board in the frame. The perspective will heighten the affect of the athlete's jumping height. If you shoot the same shot, standing, the athlete will not look heroic and your shot will be boring and stiff.
If you have High Speed Sync capability (or Hypersync w/Pocket Wizards), add counter-lighting to your shots. Put the sun over the athletes' shoulders and light their front (not usually possible during T&F, but it can sometimes be used).
Get as close to the action as you can. I'll say it again...get as close to the action as you can! At some meets I have access to place my camera directly alongside the rail on the homestretch. I place the camera as low as I can, often directly on the deck. I use a wide angle lens, prefocused on manual focus to the point I want to capture, and set the exposure settings to manual. As the athletes run by I rip off bursts of 3-5 for each athlete. I use f/5.6 or even f/8 to ensure adequate DOF as the athletes move through the focus zone. That gives me a margin for error to ensure I get the peak action with the both of the athlete's feet off the ground. Those make awesome, "superhero" shots that the athletes and parents love.
Shoot hurdles from many angles, but especially with your longest lens, straight down the track with the athletes running into your frame. Rip off burst of 3-5 as they clear each hurdle. The best shots have the athletes hands straight to the side while both legs clear the hurdle, with visible distance between the lowest point of the athlete's shoe and the hurdle. That is a micro-instant that very few can get right with a single shot. With a 1Dx and 12fps, better to rip of a burst at each hurdle. For those shots I use single point AF, and hold it directly on the athlete's face. Most experienced hurdlers are fairly fluid and don't bob their heads much.
From the shots you posted, your post processing can use quite a bit of work too. The panning shot isn't too badly executed, but it lacks any punch at all. Better post processing and perhaps a judicious crop would turn that into a fairly passable shot.
There is a lot to learn and apply to get great athletic shots, but it can be done. Number one rule is NEVER, EVER, EVER shoot standing. No matter how well you execute the technical aspects of operating the camera, your image is going to be boring and common. Think ALWAYS about simplifying and cleaning up the background. Sometimes it can't be avoided, but still...when you have to break the rule make sure you have no alternative. If you must have something in the background because of the venue, try to find an angle to put the scoreboard timer behind or next to the athletes. Give some context.
Group shots (running packs around the corner for instance) rarely work well when executed with DOF to have all runners sharp. Make a decision to focus on a single runner and drop your DOF as thin as you can. The image will still tell the story of the runner running in a pack, but it reinforces the image to make it about THAT runner. Too much DOF usually leaves the image subject-less, at least in telephoto type shots. I rarely shoot such shots with deeper DOF that I am happy with, and almost never when the athletes are in motion.