I would certainly NOT run all three -- in my view doing so would kill any chance for a good marathon and almost guarantee injury. I'll comment on these individually.
Half-marathon: would be okay if you don't race it 100%. Some will tell you 3 weeks out is fine but I think a full month would be the minimum.
22 miler: this is okay with me provided (a) your weekly mileage is at least 80-85 on average, (b) it doesn't represent your longest pre-marathon run and (c) you've run MP miles at the end of long runs at least a few times.
5K/10K: I wouldn't do this. It may not hurt your marathon but neither will it help, and if you've really been focusing on marathon training for several months you won't be in top shape for races of these distances. I don't see the point of it.